Social Choice and Welfare

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  • Kemal Kıvanç AközKemal Kıvanç Aköz
  • Alexei ZakharovAlexei Zakharov
We model costly, strategic voting in an electorate divided between a single pro-incumbent and multiple pro-opposition groups, and study the effect of the homogeneity of preferences within the opposition electorate on voter turnout. If each opposition group is represented by a separate candidate, there is a free-rider effect: the opposition turnout is lower if different opposition candidates are more substitutable. If there is a single pro-opposition candidate, the effect is the opposite under the proportional representation, and under a winner-tale-all system it depends on the size of the opposition, weighted by the intensity of preferences toward the opposition candidate. The weighted size of the opposition electorate also matters for how preference homogeneity affects incumbent vote share under proportional representation.
Zonotopes in d=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d=2$$\end{document} and d=3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d=3$$\end{document} dimensions
Zonotope inclusion
The analysis of many phenomena requires partitioning societies into groups and studying the extent at which these groups are distributed with different intensities across relevant non-ordered categorical outcomes. When the groups are similarly distributed, their members have equal chances to achieve any of the attainable outcomes. Otherwise, a form of dissimilarity between groups distributions prevails. We characterize axiomatically the dissimilarity partial order of multi-group distributions defined over categorical outcomes. The main result provides an equivalent representation of this partial order by the ranking of multi-group distributions originating from the inclusion of their zonotope representations. The zonotope inclusion criterion refines (that is, is implied by) majorization conditions that are largely adopted in mainstream approaches to multi-group segregation or univariate and multivariate inequality analysis.
The Palavas lagoon complex in S. France on the Mediterranean Sea with its coastal barrier (25 km long running SW–NE) and its fringing wetlands (Coastal lagoon area retrieved from Oxsol data base, which is a regional refinement of Corine Land Cover; background OpenStreetMap)
The overall steps of the data collection during the citizens’ workshops
The Ecosystem Services selected as the six most important after deliberation in the six different groups according RESPA. The radar plots indicate the differences in their rankings after deliberation with respect to their rankings before deliberation (based on the aggregation of the individual preferences of the group members) both for the MJ and RESPA aggregation rules. (Note for the radar plots that starting at the top with the ES ‘Flooding regulation and protection’ selected by all six groups, the selected ESs appear clockwise in the order of their MJ ranking in Table 1)
workshops valuation by the participants (averaged)
This paper describes an empiric study of aggregation and deliberation—used during citizens’ workshops—for the elicitation of collective preferences over 20 different ecosystem services (ESs) delivered by the Palavas coastal lagoons located on the shore of the Mediterranean Sea close to Montpellier (S. France). The impact of deliberation is apprehended by comparing the collectives preferences constructed with and without deliberation. The same aggregation rules were used before and after deliberation. We compared two different aggregation methods, i.e. Rapid Ecosystem Services Participatory Appraisal (RESPA) and Majority Judgement (MJ). RESPA had been specifically tested for ESs, while MJ evaluates the merit of each item, an ES in our case, in a predefined ordinal scale of judgment. The impact of deliberation was strongest for the RESPA method. This new information acquired from application of social choice theory is particularly useful for ecological economics studying ES, and more practically for the development of deliberative approaches for public policies.
In this note, we consider sufficient conditions for the uniqueness of the core partitions of coalition formation games. İnal (Soc Choice Welf 45:745–763, 2015) introduces a sufficient condition called k-acyclicity and claims that this condition is independent of another sufficient condition called top-coalition property. We show that this claim is incorrect and, in particular, k-acyclicity is equivalent to the common ranking property introduced by Banerjee et al. (Soc Choice Welf 18:135–153, 2001), which is a stronger condition than the top-coalition property.
Optimality likelihood of democracy (d), semi-democracy (sd), epistocracy (e) and semi-epistocracy (se) as a function of the mean competence and standard deviation for the normal distribution of skills and n=3,5,7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n = 3,\,5,\,7$$\end{document}. The subfigures for n=9,11,21\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n = 9,\,11,\,21$$\end{document} are in the Fig. 3 in the Appendix
The probability that the simple majority rule and the optimal weighted majority rule select the same alternative as a function of n, for different mean competence levels and different standard deviations under the truncated normal distribution of skills
In a classical “jury theorem” setting, the collective performance of a group of independent decision-makers is maximized by a voting rule that assigns weight to individuals compatibly with skills. The primary concern is that such weighted voting interferes with majoritarianism, since excessive power may be granted to a competent minority. In this paper, we address a surprisingly undertheorized issue of much significance to collective decision-making: the overlap of optimal weighted voting and the democratic, ubiquitous simple majority rule which is typically adopted in public decision-making. Running Monte Carlo simulations on the distribution of skills in large groups, our main findings are rather counterintuitive. In terms of procedure, the optimal allocation of weights is almost always democratic or “semi-democratic”, in that it satisfies or draws close to “one person, one weight”. In terms of outcome, the chosen alternative under optimal weighted voting is almost always the one that would have been selected by the simple majority rule, which satisfies “one person, one vote”. We thereby submit that the decision rules supported by the proceduralist and epistemic approaches to collective decision-making, effectively coincide more often than one would expect.
The rule q as function of n and |A|, n=2000
A policy proposal introduced by a committee member is either adopted or abandoned in favor of a new proposal after lengthy deliberations. If a proposal is abandoned, the committee member who introduced it does not cooperate in any effort to replace it. For a player, not cooperate means to vote against a proposal when the rule identifies him or her as one of those who are entitled to make a decision. The one-core is a solution concept that captures that idea. It is never empty if the committee has less than five individuals, but might be empty if there are five or more individuals. I identify a necessary and sufficient condition for the non-emptiness of the one-core no matter the number of alternatives, the preference profile or the number of players in a committee game, under any qualified majority rule.
We examine technology adoption and growth in a political economy framework where two alternative mechanisms of redistribution are on the menu of choice for the economy. One of these is a lump-sum transfer given to agents in the economy. The other is in the form of expenditure directed towards institutional reform aimed at bringing about a reduction in the cost of technology adoption in the presence of uncertainty. The choice over these mechanisms is examined under three alternative approaches to collective decision making, namely a voting mechanism, and social planning with a Benthamite and Rawlsian social welfare function respectively. We find that the extent of uncertainty, and initial inequality, working through the political economy mechanism, have a positive impact on long run average wealth levels in the economy in all settings. All economies converge to the same inequality and growth rates in the long run; however, the speed of transition is fastest with the voting mechanism and slowest in the case of social planning with the Rawlsian social welfare function. Transitional inequality is highest in the Rawlsian framework, suggesting that egalitarian objectives in collective decision making do not necessarily correspond to egalitarian outcomes for the economy.
A voting rule is monotonic if a winning candidate never becomes a loser by being raised in voters’ rankings of candidates, ceteris paribus. Plurality with a runoff is known to fail monotonicity. To see how widespread this failure is, we focus on French presidential elections since 1965. We identify mathematical conditions that allow a logically conceivable scenario of vote shifts between candidates that may lead to a monotonicity violation. We show that eight among the ten elections held since 1965 (those in 1965 and 1974 being the exceptions) exhibit this theoretical vulnerability. To be sure, the conceived scenario of vote shifts that enables a monotonicity violation may not be plausible under the political context of the considered election. Thus, we analyze the political landscape of these eight elections and argue that for two of them (2002 and 2007 elections), the monotonicity violation scenario was plausible within the conjuncture of the time.
Change of coordinates
The interim allocation set Q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {Q}$$\end{document} and utility set U\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {U} $$\end{document}
We consider a reduced-form implementation problem where two players bargain over how to allocate some resources among a finite set of social alternatives. Each player’s payoff depends on how much of the resources is allocated towards each alternative. Distributional constraints on some targeted groups of alternatives are allowed. Using a network flow approach, we provide a characterization of the reduced-form implementability condition. We show that our results can be useful to study public good problems with budget constraints where a joint implementation of private and public alternatives is possible.
In this paper, we explore the stability of the aggregation procedure of individual preferences. In particular, we propose the stability under the addition of social preference, which is a normative property of democratic collective decision making. We establish impossibility and possibility theorems for non-dictatorial aggregation procedures.
Identity utility and relative performance
Myopic equilibrium (ME) and First Best (FB) solution under Joneses dominance
a ME and FB solution with over-consumption for both agent types under Cautionary dominance. b ME and FB solution with both over- and under-consumption under Cautionary dominance
ME and FB under Cautionary dominance and elitist social preferences
In this paper, we build on theories in psychology and economics and link positional preferences to private agents’ identification with a social group, and the social norms present in that group. The purpose of our paper is to analyze behavioral, welfare, and policy implications of a link between private agents´ social identity and a risky leisure activity. Our results suggest that, when the outcome of the positional activity is uncertain, the over-consumption result that is associated with positional preferences in a deterministic framework need not apply to all agents in a social equilibrium. The reason is that agents have incentives to act with caution in order to avoid failure when the outcome of the socially valued activity is uncertain. We also show how policy can be used to improve the welfare within a social group where the risky leisure activity is positional.
We consider synchronous iterative voting, where voters are given the opportunity to strategically choose their ballots depending on the outcome deduced from the previous collective choices. We propose two settings for synchronous iterative voting, one of classical flavor with a discrete space of states, and a more general continuous-space setting extending the first one. We give a general robustness result for cycles not relying on a tie-breaking rule, showing that they persist under small enough perturbations of the behavior of voters. Then we give examples in Approval Voting of electorates applying simple, sincere and consistent heuristics (namely Laslier’s Leader Rule or a modification of it) leading to cycles with bad outcomes, either not electing an existing Condorcet winner, or possibly electing a candidate ranked last by a majority of voters. Using the robustness result, it follows that those “bad cycles” persist even if only a (large enough) fraction of the electorate updates its choice of ballot at each iteration. We complete these results with examples in other voting methods, including ranking methods satisfying the Condorcet criterion; an in silico experimental study of the rarity of preference profiles exhibiting bad cycles; and an example exhibiting chaotic behavior.
First, as student 3 has the lowest priority rank in the resulting permutation we start by swapping her priority rank with 4, then with 5 and obtain column (b) below. Then, as student 2 has the second lowest priority rank in the resulting permutation, we swap the priority ranks of students 2 with 4, then 2 with 5 and obtain column (c). Lastly, we swap the priority ranks of 1 and 4 to obtain the desired permutation
School districts commonly ration public school seats based on students’ preferences and schools’ priorities. Priorities reflect the school districts’ objectives for reducing busing costs (walk-zone priority) or utilizing siblings’ learning spillovers (sibling priority). I develop a simple modification of the well-studied Top Trading Cycles mechanism that matches schools to higher priority students while preserving the mechanism’s desirable efficiency and incentives properties.
Voters’ and senators’ positions with and without STVO. Note: Left-hand graph shows average senatorial positions by party and STVO status. Right-hand graph displays self-declared average voter positions by STVO presence. Senators’ positions correspond to the first dimension of DW-NOMINATE, a multidimensional scaling application developed by Poole and Rosenthal (2015). Voters’ positions are the first dimension of Enns and Koch (2013)’s dynamic scale of voters’ policy “moods”. Data on the presence of the STVO on state ballots are from Gorelkina et al. (2019). All positional data are projected onto a left (0) right (100) axis. State-level data on voters’ partisanship and positions calculated at the beginning of each Congressional term. See Gorelkina et al. (2019) for a full description of the data used to generate each graph
Party-candidate association in elections. Note: Figure shows the availability and ease of voting a straight ticket in different electoral systems and the implied strength of association between parties and their candidates, from no association (left) to full association (right)
This paper explores the effects of the straight-ticket voting option (STVO) on the positions of politicians. STVO, present in some US states, allows voters to select one party for all partisan elections listed on the ballot, as opposed to filling out each office individually. We analyse the effects of STVO on policy-making by building a model of pre-election competition. STVO results in greater party loyalty of candidates, while increasing the weight of non-partisan voters’ positions in candidate selection. This induces an asymmetric effect on vote shares and implemented policies in the two-party system.
BO marginal tax rates. Although all lines should technically be perfectly flat, some of them are drawn as squiggles to distinguish the marginal tax rates for the different values of σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma$$\end{document}. The marginal rate for σ=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma =1$$\end{document} equals 0.7 for incomes up to $3,154 (this is barely visible in the top left corner of the figure) and jumps to 0.4 at income $925,653 (this is not shown in the figure)
BO average tax rates. The average rates for σ=0.25\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma = 0.25$$\end{document} and σ=0.5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma =0.5$$\end{document} monotonically increase towards 0.7 and 0.5, respectively, as income increases beyond the values shown in the figure. The average rate for σ=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma =1$$\end{document} monotonically declines from 0.313 to 0.3 between incomes $32,878 and $925,653 and monotonically increases towards 0.4 at higher incomes
I numerically compute Borda-optimal, i.e., optimal based on the Borda count as the normative criterion, labour-income tax schedules for the United States. I do so in the context of a Mirrlees-style model with quasilinear preferences and a constant elasticity of labour supply. Because the Borda count is defined for finitely many alternatives, the computations restrict attention to a finite subset of the set of continuous, piecewise linear tax schedules with (in the baseline analysis) four or fewer pieces.
A social choice correspondence is Nash self-implementable if it can be implemented in Nash equilibrium by a social choice function that selects from it as the game form. We provide a complete characterization of all unanimous and anonymous Nash self-implementable social choice correspondences when there are two agents or two alternatives. For the case of three agents and three alternatives, only the top correspondence is Nash self-implementable. In all other cases, every Nash self-implementable social choice correspondence contains the top correspondence and is contained in the Pareto correspondence. In particular, when the number of alternatives is at least four, every social choice correspondence containing the top correspondence plus the intersection of the Pareto correspondence with a fixed set of alternatives, is self-implementable.
The separating (S) equilibrium
The pooling (P) equilibrium
The mixed-strategy, semi-separating, (M) equilibrium
A reelection-seeking politician makes a policy decision that can reveal her private information. This information bears on whether her political orientation and capabilities will be a good fit to future circumstances. We study how she may choose inappropriate policies to hide her information, even in the absence of specific conflicts of interests, and how voters’ conformism affects her incentives to do so. Conformism is independent from policies and from voters’ perceptions. Yet we identify a ‘conformism advantage’ for the incumbent that exists only when there is also an incumbency advantage. Conformism changes the incentives of the incumbent and favors the emergence of an efficient, separating equilibrium. It may even eliminate the pooling equilibrium (that can consist in inefficient persistence). Conformism has a mixed impact on social welfare however: it improves policy choices and the information available to independent voters, but fosters inefficient reelection in the face of a stronger opponent. When the incumbent is ‘altruistic’ and values social welfare even when not in power, she partly internalizes this latter effect. The impact of conformism is then non monotonous.
We consider collective choice problems where the set of social outcomes is a Cartesian product of finitely many finite sets. Each individual is assigned a two-level preference, defined as a pair involving a vector of strict rankings of elements in each of the sets and a strict ranking of social outcomes. A voting rule is called (resp. weakly) product stable at some two-level preference profile if every (resp. at least one) outcome formed by separate coordinate-wise choices is also an outcome of the rule applied to preferences over social outcomes. We investigate the (weak) product stability for the specific class of compromise solutions involving q-approval rules, where q lies between 1 and the number I of voters. Given a finite set X and a profile of I linear orders over X, a q-approval rule selects elements of X that gathers the largest support above q at the highest rank in the profile. Well-known q-approval rules are the Fallback Bargaining solution (q=I) and the Majoritarian Compromise (q=⌈(I/2)⌉). We assume that coordinate-wise rankings and rankings of social outcomes are related in a neutral way, and we investigate the existence of neutral two-level preference domains that ensure the weak product stability of q-approval rules. We show that no such domain exists unless either q=I or very special cases prevail. Moreover, we characterize the neutral two-level preference domains over which the Fallback Bargaining solution is weakly product stable.
Profiles P′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P'$$\end{document}, P′′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P''$$\end{document}, P1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P^1$$\end{document}, and P2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P^2$$\end{document} in Case 2 of Proof of [1] of Theorem 2
We introduce a new condition for social choice functions, called “equal treatment of congruent distributions.” It requires some invariance between two preference profiles that share a type of congruity property with respect to the associated distributions of votes. It also implies two equal treatment conditions: one is a natural weakening of anonymity, which is the most standard equal treatment condition for individuals, and the other is a natural weakening of neutrality, which is the most standard equal treatment one for alternatives. Thus, equal treatment of congruent distributions plays the role of weak equal treatment conditions both for individuals and for alternatives. As our main results, we characterize a class of social choice functions that satisfy equal treatment of congruent distributions and some mild positive responsiveness conditions, and it is shown to coincide with the class of tie-breaking plurality rules, which are selections of the well-known plurality rule.
Round-robin tournaments with an endogenous schedule
Two versions of the alternative tournament model
We propose a novel tournament design that incorporates some properties of a round-robin tournament, a Swiss tournament, and a race. The new design includes an all-play-all structure with endogenous scheduling and a winning threshold. Considering a standard round-robin tournament as a baseline model, we first characterize the equilibrium strategies in round-robin tournaments with exogenous and endogenous schedules. Afterward, following an equilibrium analysis of the new tournament design, we compare thirty-six tournament structures inherent in our model with round-robin tournaments on the basis of expected equilibrium effort per battle. We show that a round-robin tournament with an endogenous schedule outperforms all the other tournament structures considered here. We further note that if expected total equilibrium effort is used as a comparison criterion instead, then the new tournament design has a potential to improve upon round-robin tournaments.
Budget-constrained quasi-linear preference. A point ra\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r_a$$\end{document} in the axis corresponding to room a represents the bundle (ra,a)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(r_a,a)$$\end{document}. Solid lines connecting axes represent indifference curves, i.e., they connect bundles that are indifferent for the agent
The current practice of envy-free rent division, led by the fair allocation website Spliddit, is based on quasi-linear preferences. These preferences rule out agents’ well documented financial constraints. To resolve this issue we consider an extension of the quasi-linear domain that admits differences in agents’ marginal disutility of paying rent below and above a given reference, i.e., a soft budget. We construct a polynomial algorithm to calculate a maxmin utility envy-free allocation, and other related solutions, in this domain.
In their article ‘Liberal political equality implies proportional representation’, which was published in Social Choice and Welfare 33(4):617–627 in 2009, Eliora van der Hout and Anthony J. McGann claim that any seat-allocation rule that satisfies certain ‘Liberal axioms’ produces results essentially equivalent to proportional representation. We show that their claim and its proof are wanting. Firstly, the Liberal axioms are only defined for seat-allocation rules that satisfy a further axiom, which we call Independence of Vote Realization (IVR). Secondly, the proportional rule is the only anonymous seat-allocation rule that satisfies IVR. Thirdly, the claim’s proof raises the suspicion that reformulating the Liberal axioms in order to save the claim won’t work. Fourthly, we vindicate this suspicion by providing a seat-allocation rule which satisfies reformulated Liberal axioms but which fails to produce results essentially equivalent to proportional representation. Thus, the attention that their claim received in the literature on normative democratic theory notwithstanding, van der Hout and McGann have not established that liberal political equality implies proportional representation.
Contributions of groups i and j as a function of cI,i\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c_{I,i}$$\end{document} (cJ,j=cI,j=cJ,i=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c_{J,j}=c_{I,j}=c_{J,i}=1$$\end{document})
Equilibrium of the pricing stage game for different pairs V,vcI,j=1.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\{ V,v\right\} \, \left( c_{I,j}=1\right) .$$\end{document}
We study a game with two candidates and two interest groups. The groups offer two kinds of costly contributions to achieve political influence: (a) pre-election campaign contributions to their favourite candidates that increase their probability of winning the election and (b) post-election lobbying contributions to the winning candidate to affect the implemented policy. The candidates are the first to act by strategically choosing the lobbying prices they will charge the groups if they are elected. We characterise the equilibrium values of the lobbying prices set by the candidates as well as the equilibrium levels of the campaign and lobbying contributions chosen by the groups. We show, endogenously, that in the case with symmetric groups and symmetric politicians, a candidate announces to charge the group that supports her in the election a lower lobbying price, justifying this way the preferential treatment to certain groups from the politicians in office. We also consider two extensions (asymmetric groups and politicians who do not commit to the announced prices) and show that the results of the benchmark model hold under specific conditions.
We study the design of a fair family policy in an economy where parenthood is regarded either as desirable or as undesirable, and where there is imperfect fertility control, leading to involuntary childlessness/parenthood. Using an equivalent consumption approach in the consumption-fertility space, we show that the identification of the worst-off individuals depends on how the social evaluator fixes the reference fertility level. Adopting the ex post egalitarian criterion (giving priority to the worst off in realized terms), we study the compensation for involuntary childlessness/parenthood. Unlike real-world family policies, the fair family policy does not always involve positive family allowances, and may also include positive childlessness allowances. Our results are robust to assuming asymmetric information and to introducing Assisted Reproductive Technologies.
Average group contribution over periods
Distributions of individual contributions: homogeneous
Distributions of individual contributions: heterogeneous
Reward (reward vote) received across different deviation ranges in the peer (vote) situation
This paper conducts a laboratory experiment to examine the effectiveness of majority-vote reward mechanism on cooperation, and to compare its effects with that of peer reward and no reward in the voluntary contribution mechanism. According to the experimental result, it shows that whether individuals have homogeneous or heterogeneous marginal per capita return of the public good, the majority-vote reward mechanism is significantly effective in facilitating cooperation.
An example of an extensive form representing cut and choose
Agent Blue only values the pieces shown in blue
Obvious manipulations for agent blue (black arrow), supporting preferences for the other agent (red), final allocation received by blue agent (green)
Banach-Knaster is obviously manipulable (The manipulation by agent 2 at node h corresponds to the thick edge)
A mixed cake in which leftmost-leaves is OM. Good parts of the cake appear in blue, bad parts in red
In the classical cake-cutting problem, strategy-proofness is a very costly requirement in terms of fairness: for n=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=2$$\end{document} it implies a dictatorial allocation, whereas for n≥3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\ge 3$$\end{document} it implies that one agent receives no cake. We show that a weaker version of this property recently suggested by Troyan and Morril (J Econ Theory 185:104970, 2019) is compatible with the fairness property of proportionality, which guarantees that each agent receives 1/n of the cake. Both properties are satisfied by the leftmost-leaves mechanism, an adaptation of the Dubins–Spanier moving knife procedure. Most other classical proportional mechanisms in the literature are obviously manipulable, including the original moving knife mechanism and some other variants of it.
Zero poverty and two-candidate equilibria. The space of potential candidates is depicted in gray, while the space of voters is the black horizontal line. The blue line represents all the citizens (voters and potential candidates) that are indifferent between candidates i and k
Swing voters and poverty lines. For candidates i and k, there are at most four cut-offs: one poor swing voter, ω∗P(i,k)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega ^{*P}(i,k)$$\end{document}, one rich, ω∗R(i,k)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega ^{*R}(i,k)$$\end{document}, and the poverty lines ω0(i)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega ^{0}(i)$$\end{document} and ω0(k)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega ^{0}(k)$$\end{document}. The resulting groups are very poor, poor middle class, poor & rich, rich middle class, and very rich
Inequality growth and demographics. Scatter plot of Gini five year log-changes (y-axis) on share of female (x-axis, left figure) and those aged 25–35 (x-axis, right figure) in the working age population. All residualized with respect to year averages. Best-fit line in red
Inequality and poverty. Municipality level five year inequality and poverty log-differences. Inequality measured using the Gini index, poverty is the proportion of the municipality population with income lower than 60% the national median. Inequality and poverty growth figures depicted are residuals from regressions with year dummies
We study the use of social expenditures and regulation for redistribution. When regulated goods are essential in the consumption bundle of the poor, a high poverty rate creates incentives to increase redistribution through regulation. By contrast, inequality directs redistribution towards social expenditures. We propose a theoretical model that captures the trade-off between these two redistributive policies and test the model implications with a novel municipality dataset on income and local government policies. Theory predicts and empirical evidence supports that failing to account for poverty biases the effect of inequality on redistribution. Our evidence also reflects the positive connection between poverty and the use of regulation for redistribution.
Immediate Pareto-dominance graph when q=4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q=4$$\end{document}
We study the aggregation of a couple’s preferences over their respective jobs when the couple enters a centralized labor market jointly, such as the market for hospital residencies. In such markets couples usually need to submit a joint preference ordering over pairs of jobs and thus we are interested in preference aggregation rules which start with two individual preference orderings over single jobs and produce a preference ordering of pairs of jobs. We first study the Lexicographic and the Rank-Based Leximin aggregation rules, as well as a large class of preference aggregation rules which contains these two rules. Then we propose a smaller family of parametric aggregation rules, the k-Lexi-Pairing rules, which call for a systematic way of compromising between the two partners. The parameter k indicates the degree to which one partner is prioritized, with the most equitable Rank-Based Leximin rule at one extreme and the least equitable Lexicographic rule at the other extreme. Since couples care about geographic proximity, a parametric family of preference aggregation rules which build on the k-Lexi-Pairing rules and express the couple’s preference for togetherness is also identified. We provide axiomatic characterizations of the proposed preference aggregation rules.
The set of awards vectors and the AA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text {AA}}$$\end{document} rule for a two-claimant problem
The set of awards vectors X(3, (1, 2, 2)) and its centroid
Claims arranged in ascending order on the interval [0, d(N)]
The schedules of awards of the AA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text {AA}}$$\end{document} rule for two-claimant problems
The schedules of awards of the AA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text {AA}}$$\end{document} rule for d=(2,4,5)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d=(2,4,5)$$\end{document}
Given a claims problem, the average-of-awards rule (AA) selects the expected value of the uniform distribution over the set of awards vectors. The AA rule is the center of gravity of the core of the coalitional game associated with a claims problem, so it corresponds to the core-center. We show that this rule satisfies a good number of properties so as to be included in the inventory of division rules. We also provide several representations of the AA rule and a procedure to compute it in terms of the parameters that define the problem.
The search for a compromise between marginalism and egalitarianism has given rise to many discussions. In the context of cooperative games, this compromise can be understood as a trade-off between the Shapley value and the Equal division value. We investigate this compromise in the context of multi-choice games in which players have several activity levels. To do so, we propose new extensions of the Shapley value and of the Equal division value to multi-choice games. Contrary to the existing solution concepts for multi-choice games, each one of these values satisfies a Core condition introduced by Grabisch and Xie (Math Methods Oper Res 66(3):491–512, 2007), namely Multi-Efficiency. We compromise between marginalism and egalitarianism by introducing the multi-choice Egalitarian Shapley values, computed as the convex combination of our extensions. To conduct this study, we introduce new axioms for multi-choice games. This allows us to provide an axiomatic foundation for each of these values.
We report the results of a vignette study with an online sample of the German adult population in which we analyze the interplay between need, equity, and accountability in third-party distribution decisions. We asked participants to divide firewood between two hypothetical persons who either differ in their need for heat or in their productivity in terms of their ability to chop wood. The study systematically varies the persons' accountability for their neediness as well as for their productivity. We find that participants distribute significantly fewer logs of wood to persons who are held accountable for their disadvantage. Independently of being held accountable or not, the needier person is partially compensated with a share of logs that exceeds her contribution, while the person who contributes less is given a share of logs smaller than her need share. Moreover, there is a domain effect in terms of participants being more sensitive to lower contributions than to greater need.
Finding support for cooperative solution concepts through non-cooperative bargaining models is the basic idea of the Nash program. The present paper pursues precisely this goal. In particular, it tries to find support for a newly introduced solution concept, the Mid-central Core, for transferable utility games in characteristic function form. It does so through a standard alternating offers model, the Burning Coalition Bargaining model, where discounting is substituted by the risk of partial breakdown of negotiations. However, it presents two significant novelties. First, the risk of partial breakdown differs from the standard characterization that it has in the dedicated literature since the rejection of a proposal triggers the possibility of dissolution of the worth of the proposed coalition, rather than the exclusion of some players. Secondly, a rejection is followed by a second, one-shot, round of negotiations happening in the same time period. It is shown that it exists a strategy profile according to which the Mid-central Core is supported in stationary sub-game perfect equilibrium for any value of the parameter determining the risk of partial breakdown in the interval (0,1).
Effect of opinion leader’s influence on competence, cinit=0.3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c_{init}=0.3$$\end{document}
Effect of opinion leader’s influence on competence, cinit=0.6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c_{init}=0.6$$\end{document}
Effect of opinion leader’s influence on dependence
Effect of opinion leader’s influence on the quality of the collective decision (cinit=0.6,m=5,a=1.5,b=0.5)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(c_{init}=0.6, m=5, a=1.5, b=0.5)$$\end{document}
Effect of the expert opinion leader on the quality of the collective decision (c∗=0.7,cinit=0.6,m=5,a=3,b=3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(c^*=0.7, c_{init}=0.6, m=5, a=3, b=3)$$\end{document}. U(∞)=0.7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U(\infty )=0.7$$\end{document}; U(0)=0.77\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U(0)=0.77$$\end{document}; U(0.11)=0.83\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U(0.11)=0.83$$\end{document}
The purpose of this paper is to illustrate, formally, an ambiguity in the exercise of political influence. To wit: A voter might exert influence with an eye toward maximizing the probability that the political system (1) obtains the correct (e.g. just) outcome, or (2) obtains the outcome that he judges to be correct (just). And these are two very different things. A variant of Condorcet’s Jury Theorem which incorporates the effect of influence on group competence and interdependence is developed. Analytic and numerical results are obtained, the most important of which is that it is never optimal—from the point-of-view of collective accuracy—for a voter to exert influence without limit. He ought to either refrain from influencing other voters or else exert a finite amount of influence, depending on circumstance. Philosophical lessons are drawn from the model, to include a solution to Wollheim’s “paradox in the theory of democracy”.
College admission process
(a) L-type students. (b) H-type students. No financial aid: Each box represents each type of students and δ=0.05\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta =0.05$$\end{document}. The dashed areas represent the set of students who exert effort; the lightly shaded areas represent the set of students that receive offers from both A and B; the white areas represent the set of students that receive offers only from B; and the dark shaded areas represent those who do not receive any offer from the two selective colleges. The upper right corner areas separated by thick lines represent those who enroll in A. The areas other than this area and the dark shaded areas represent those who enroll in B. We obtain xA∗=0.5593\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_A^*=0.5593$$\end{document} and xB∗=0.3833\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_B^*=0.3833$$\end{document}
(a) L-type students. (b) H-type students. Need-based financial aid: The upper right corner area separated by thick lines in the left box represents those who receive need-based aid from A (FA∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F^*_A$$\end{document} per student). The area in the left box other than this area and the dark shaded area represents those who receive need-based aid from B (FB∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F^*_B$$\end{document} per student). We obtain xA∗=0.5633\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_A^*=0.5633$$\end{document} and xB∗=0.3833\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_B^*=0.3833$$\end{document}, while FA∗=1.511\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F^*_A=1.511$$\end{document} and FB∗=1.489\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F^*_B=1.489$$\end{document}
(a) L-type students. (b) H-type students. Merit-based financial aid: the amount of merit-based aid per student is 1.667 at each college. In addition to admission cutoffs, the colleges have cutoffs for aid, mA∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_A^*$$\end{document} and mB∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_B^*$$\end{document}. We obtain xA∗=0.476\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_A^*=0.476$$\end{document}, xB∗=0.383\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_B^*=0.383$$\end{document}, mA∗=0.815\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_A^*=0.815$$\end{document} and mB∗=0.744\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_B^*=0.744$$\end{document}
(a) L-type students. (b) H-type students. Equilibrium choice of financial aid when yAB(-F-cH)<y¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${y^{AB}(-F-c_H)<{\overline{y}}}$$\end{document}: when college A has a higher ranking than college B, all students on top choose to get into A. Some students who can get into A only if they exert effort, however, are willing to switch to college B if B offers sufficient aid. To recruit these students, college B chooses merit-based aid. To retain them, on the other hand, college A chooses need-based aid. We obtain xA∗=0.7146\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_A^*=0.7146$$\end{document}, FA∗=1.491\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F_A^*=1.491$$\end{document}, xB∗=0.383\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_B^*=0.383$$\end{document}, mB∗=0.5667\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_B^*=0.5667$$\end{document}, and F=1.667\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F=1.667$$\end{document}
In college admission, financial aid plays an important role in students’ enrollment decision as well as their preparation for college application. We analyze how different types of financial aid affect these decisions and admission outcomes. We consider two financial aid regimes—need-based and merit-based—in a simple college admission model and characterize respective equilibria. We find that a more competitive college has a higher admission cutoff under a need-based regime than under a merit-based regime. A less competitive college, on the other hand, benefits from a merit-based regime as it admits students with a higher average ability than it does under no aid. We next allow colleges to choose their own financial aid system so as to account for a stylized fact in the US college admissions. We show that when one college is ranked above the other, it is a dominant strategy for the higher-ranked college to offer need-based aid and for the lower-ranked college to offer merit-based aid.
We use a model of impressionable voters to study multi-candidate elections under different electoral rules. Instead of maximizing expected utility, voters cast their ballots based on impressions. We show that, under each rule, there is a monotone relationship between voter preferences and vote measures. The nature of this relationship, however, varies by electoral rule. Vote measures are biased upwards for socially preferred candidates under plurality rule, but biased downwards under negative plurality. There is no such bias under approval voting or Borda count. Voters always elect the socially preferred candidate in two-way races for any electoral rule. In multi-candidate elections, however, the ability to elect a Condorcet winner varies by rule. The results show that multi-candidate elections can perform well even if voters follow simple behavioral rules. The relative performance of specific electoral institutions, however, depends on the assumed behavioral model of voting.
Illustration of type profiles for each subset of the partition. Each green dot represents an equilibrium inXand each red triangle represents an equilibrium not inX
We study criteria that compare mechanisms according to a property (e.g., Pareto efficiency or stability) in the presence of multiple equilibria. The multiplicity of equilibria complicates such comparisons when some equilibria satisfy the property while others do not. We axiomatically characterize three criteria. The first criterion is intuitive and based on highly compelling axioms, but is also very incomplete and not very workable. The other two criteria extend the comparisons made by the first and are more workable. Our results reveal the additional robustness axiom characterizing each of these two criteria.
Probability of going for a second round
Probability of stopping in each round, with discount = 3
Probability of stopping in each round, with discount = 5
We investigate cases of preference change in the context of cake-cutting problems. In some circumstances, believing that some other player can be credited with a particular preference structure triggers a preference shift by imitation. As a result of this, players may experience regret. However, in typical examples the extent of the change (and the ensuing regret) cannot be anticipated, so players cannot adjust their behavior beforehand. Our goal is to describe the phenomenon, provide a formal model for it, and explore circumstances and allocation procedures that may alleviate some of its negative consequences. In the face of utility shifts we propose a new criterion for fairness, which we dub Ratifiability; in a ratifiable allocation rational players are happy to stick to their choices, in spite of the changes in utilities they may experience. We argue that this embodies a sense of fairness that is not captured by other properties of fair allocation.
We consider the strategy-proof rules for reallocating individual endowments of an infinitely divisible good when agents’ preferences are single-peaked. In social endowment setting, the seminal work established by Sprumont (Econometrica 59:509–519, 1991) proves that the uniform rule is the unique one which satisfies strategy-proofness, efficiency, and envy-freeness. However, the uniform rule is not so appealing in our model since it disregards the differences in individual endowments. In other words, the uniform rule is not individually rational. In this paper, we propose a new rule named the uniform proportion rule. First, we prove that it is the unique rule which satisfies strategy-proofness, efficiency, and envy-freeness on proportion and we show that it is individually rational. Then, we show that our rule is indeed a member of the class of sequential allotment rules characterized by Barberà et al. (Games Econ Behav 18:1–21, 1997).
The doctrinal paradox is analysed from a probabilistic point of view assuming a simple parametric model for the committee’s behaviour. The well known premise-based and conclusion-based majority rules are compared in this model, by means of the concepts of false positive rate (FPR), false negative rate (FNR) and Receiver Operating Characteristics (ROC) space. We introduce also a new rule that we call path-based, which is somehow halfway between the other two. Under our model assumptions, the premise-based rule is shown to be the best of the three according to an optimality criterion based in ROC maps, for all values of the model parameters (committee size and competence of its members), when equal weight is given to FPR and FNR. We extend this result to prove that, for unequal weights of FNR and FPR, the relative goodness of the rules depends on the values of the competence and the weights, in a way which is precisely described. The results are illustrated with some numerical examples.
A three-dimensional representation of the possible opinions and decision function in Φ0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Phi _0$$\end{document}
A three-dimensional representation of the possible opinions and decision function in Φ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Phi _1$$\end{document}
A three-dimensional representation of the possible opinions and decision function in Φ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Phi _2$$\end{document}
The problem of no hands concerns the existence of so-called responsibility voids: cases where a group makes a certain decision, yet no individual member of the group can be held responsible for this decision. Criteria-based collective decision procedures play a central role in philosophical debates on responsibility voids. In particular, the well-known discursive dilemma has been used to argue for the existence of these voids. But there is no consensus: others argue that no such voids exist in the discursive dilemma under the assumption that casting an untruthful opinion is eligible. We argue that, under this assumption, the procedure used in the discursive dilemma is indeed immune to responsibility voids, yet such voids can still arise for other criteria-based procedures. We provide two general characterizations of the conditions under which criteria-based collective decision procedures are immune to these voids. Our general characterizations are used to prove that responsibility voids are ruled out by criteria-based procedures involving an atomistic or monotonic decision function. In addition, we show that our results imply various other insights concerning the logic of responsibility voids.
Consider two principles for social evaluation. The first, “laissez-faire”, says that mean-preserving redistribution away from laissez-faire incomes should be regarded as a social worsening. This principle captures a key aspect of libertarian political philosophy. The second, weak Pareto, states that an increase in the disposable income of each individual should be regarded as a social improvement. We show that the combination of the two principles implies that total disposable income ought to be maximized. Strikingly, the relationship between disposable incomes and laissez-faire incomes must therefore be ignored, leaving little room for libertarian values.
Frequencies of individual Yes votes in the eight repetitions of each game sequence
Screenshot of the strategy method applied in the sequential game for position 3 in T1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_1$$\end{document}
Game tree with decision frequencies for the sequence 1 (P1+,P2+,P3-,P4-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_1^+,P_2^+,P_3^-,P_4^-$$\end{document}) from T2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_2$$\end{document}. Note: Pi+(-)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_i^{+(-)}$$\end{document} denotes a positive (negative) voter in position i. Subgame perfect moves in bold lines. Broken lines indicate information sets. Percentages rest on 176 decisions by 22 subjects in the previous node/information set. Average total frequency of deviations from subgame perfect equilibrium is 27%. Blue denotes anger and green solidarity. There are no strong anger nodes and no weak solidarity information sets in this game tree
Game tree with decision frequencies for the sequence 5 (P1+,P2+,P3+,P4-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_1^+,P_2^+,P_3^+,P_4^-$$\end{document}) from T1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_1$$\end{document}. Note: Pi+(-)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_i^{+(-)}$$\end{document} denotes a positive (negative) voter in position i. Subgame perfect moves in bold lines. Broken lines indicate information sets. Percentages rest on 176 decisions by 22 subjects in the previous node/information set. Average total frequency of deviations from subgame perfect equilibrium is 28%. Dark blue colored nodes denote strong anger and light blue color denotes weak anger information sets. Green denotes solidarity. There are only strong solidarity nodes and no weak solidarity information sets in this game tree
When including outside pressure on voters as individual costs, sequential voting (as in roll call votes) is theoretically preferable to simultaneous voting (as in recorded ballots). Under complete information, sequential voting has a unique subgame perfect equilibrium with a simple equilibrium strategy guaranteeing true majority results. Simultaneous voting suffers from a plethora of equilibria, often contradicting true majorities. Experimental results, however, show severe deviations from the equilibrium strategy in sequential voting with not significantly more true majority results than in simultaneous voting. Social considerations under sequential voting— based on emotional reactions toward the behaviors of the previous players—seem to distort subgame perfect equilibria.
Generic path diagram for an unconditional latent class model
Latent class analysis (LCA) model for the life circumstances typology
The (1) Illustration of the initial data structure; (2) illustration of the same dataset, as the input for the model; (3) illustration the output of the LCA model
Elbow plot of Information Criteria. n = 60,000 subsample. The lowest value indicated the optimal number of classes
Elbow plot of Information Criteria. n = 60,000 subsample. The lowest value indicated the optimal number of classes
Policymakers are generally most concerned about improving the lives of the worst-off members of society. Identifying these people can be challenging. We take various measures of subjective wellbeing (SWB) as indicators of the how well people are doing in life and employ Latent Class Analysis to identify those with greatest propensity to be among the worst-off in a nationally representative sample of over 215,000 people in the United Kingdom. Our results have important implications for how best to analyse data on SWB and who to target when looking to improve the lives of those with the lowest SWB (The authors owe a massive debt of gratitude to the Office for National Statistics for their support throughout this research. We are particularly grateful to Dawn Snape and Eleanor Rees for their valuable comments on earlier drafts of this paper, to Salah Mehad for the thorough review of methodology, and to Vahe Nafilyan for advice on clustering analysis. We also thank the anonymous reviewers for the very helpful comments. Thank you all very much.).
This paper explores the possibility, in case of belief and taste heterogeneity, to aggregate individual preferences through a deliberation process enabling society to reach a consensus. However, we show that the same deliberation process, even characterized by a convergent matrix, may lead to different consensus depending on the updating rule which is chosen by individuals, i.e., deliberation is sufficient to determine social preferences but not univocally. Then, we prove that the Pareto condition allows to choose from possible consensus the one whereby social deliberated beliefs and tastes are of a utilitarian shape.
This paper examines the implications of habit formation in private and public goods consumption for the Pareto-efficient provision of public goods, based on a two-period model with nonlinear taxation. Under weak leisure separability, and if the public good is a flow-variable such that the government directly decides on the level of the public good in each period, habit formation leads to a modification of the policy rule for public good provision if, and only if, the degrees of habituation differ for private and public good consumption. By contrast, if the public good supply is time-invariant, the presence of habit formation generally alters the policy rule for public good provision.
We propose new axiomatizations of the core and three related solution concepts that also provide predictions for (classes of) games in which the core itself is empty. Our results showcase the importance of the reduced game formulation and identify the corresponding converse consistency property as the differentiating characteristic between the core and its various extensions. Existing axiomatizations of the core and similar concepts include the required form of feasibility in the generic definition of a solution concept and/or are restricted to the domain of games for which existence is guaranteed. We dispense of both practices, thus opening up the possibility of comparing, via basic axioms, solution concepts that have different feasibility constraints and domains.
Payoff function for technologies A and B
Natural resources such as water, for which the availability to users is random, are often shared according to predefined rules. What determines users’ choice of a sharing rule? To answer this question, we designed an experiment in which subjects: (1) vote on sharing rules; (2) choose the technology that transforms the resource into payoffs; and (3) respond to a survey on their adhesion to principles of fairness. We find that although subjects tend to vote for the sharing rule that is aligned with their self-interest, they become more egalitarian if they report their views on the fairness principles before voting. Furthermore, the adhesion to fairness principles affects the subjects’ votes not directly but rather indirectly through the choice of technology.
We consider restricted domains where each individual has a domain of preferences containing some partial order. This partial order might differ for different individuals. Necessary and sufficient conditions are formulated under which these restricted domains admit unanimous, strategy-proof and non-dictatorial choice rules.
Top-cited authors
Piotr Faliszewski
  • AGH University of Science and Technology in Kraków
Piotr Skowron
  • University of Warsaw
Arkadii M. Slinko
  • University of Auckland
Toby Walsh
  • UNSW Sydney
Haris Aziz
  • National ICT Australia Ltd