ArticlePDF Available

Frequency of monotonicity failure under Instant Runoff Voting: Estimates based on a spatial model of elections

Authors:

Abstract and Figures

It has long been recognized that Instant Runoff Voting (IRV) suffers from a defect known as nonmonotonicity, wherein increasing support for a candidate among a subset of voters may adversely affect that candidate’s election outcome. The expected frequency of this type of behavior, however, remains an open and important question, and limited access to detailed election data makes it difficult to resolve empirically. In this paper, we develop a spatial model of voting behavior to approach the question theoretically. We conclude that monotonicity failures in three-candidate IRV elections may be much more prevalent than widely presumed (results suggest a lower bound estimate of 15 % for competitive elections). In light of these results, those seeking to implement a fairer multi-candidate election system should be wary of adopting IRV.
Content may be subject to copyright.
Public Choice (2014) 161:1–9
DOI 10.1007/s11127-013-0118-2
Frequency of monotonicity failure under Instant Runoff
Voting: estimates based on a spatial model of elections
Joseph T. Ornstein ·Robert Z. Norman
Received: 5 October 2012 / Accepted: 7 September 2013 / Published online: 17 October 2013
© Springer Science+Business Media New York 2013
Abstract It has long been recognized that Instant Runoff Voting (IRV) suffers from a defect
known as nonmonotonicity, wherein increasing support for a candidate among a subset of
voters may adversely affect that candidate’s election outcome. The expected frequency of
this type of behavior, however, remains an open and important question, and limited access
to detailed election data makes it difficult to resolve empirically. In this paper, we develop
a spatial model of voting behavior to approach the question theoretically. We conclude that
monotonicity failures in three-candidate IRV elections may be much more prevalent than
widely presumed (results suggest a lower bound estimate of 15 % for competitive elections).
In light of these results, those seeking to implement a fairer multi-candidate election system
should be wary of adopting IRV.
Keywords Voting theory ·Instant Runoff Voting ·Agent-based modeling ·Monotonicity
JEL Classification D72
1 Introduction
Instant Runoff Voting (IRV) is a ranked-ballot voting system that selects a single winner
by successively eliminating the candidate with the fewest first place votes until a single
candidate receives a majority. IRV, like many systems that employ a successive-elimination
procedure, violates the monotonicity criterion (Smith 1973), meaning there exist some con-
ditions under which increasing the support for a candidate (without changing the voters’
rankings for any of the other candidates) would be harmful to that candidate.
J.T. Ornstein (B)
Department of Political Science, University of Michigan, 5700 Haven Hall, 505 South State Street,
Ann Arbor, MI 48109-1045, USA
e-mail: ornstein@umich.edu
R.Z. Norman
Department of Mathematics, Dartmouth College, 340 Kemeny Hall, Hanover, NH 03755, USA
2 Public Choice (2014) 161:1–9
Fishburn and Brams (1983) describe a paradox that may result from this defect, which
they term the “more-is-less paradox”. This paradox, which we will refer to as a monotonicity
failure, is characterized as a situation in which the IRV winner would lose if ranked higher
by some subset of voters. The converse, an election in which the IRV loser would win if
ranked lower by some subset of voters, is also a type of monotonicity failure. We term the
former paradox an upward monotonicity failure, and the latter a downward monotonicity
failure. In this paper, we will focus exclusively on the prevalence of upward monotonicity
failures under IRV, leaving downward monotonicity failure as a topic for future research.
How often could we reasonably expect to observe this behavior in real-world IRV elec-
tions? One study (Allard 1996) suggests that, if the United Kingdom adopted IRV for its
general elections, this paradox would occur only about once per century. If this were true,
then the monotonicity criterion would be cause for little practical concern. However, more
recent theoretical work on the topic (Lepelley et al. 1996;Norman2006,2012; Miller 2012)
finds that the proportion of possible IRV elections that exhibit a monotonicity paradox is
non-trivial.
Here we build on this body of work by estimating IRV’s monotonicity failure rate in the
context of a spatial model of voter behavior. This method allows us to avoid the assumption
that all electoral outcomes are equiprobable, and to explore the conditions under which IRV
may be more or less vulnerable to monotonicity failure.
2 The 2009 Burlington mayoral election: a case study
Before introducing the model, we present a case study from the 2009 mayoral election in
Burlington, VT, which illustrates the key features of an upward monotonicity failure. Table 1
reports the ballot results for the three candidates remaining before the final elimination—the
Republican (R), Democrat (D), and Progressive (P).
The Republican candidate had the most first-place votes, with 3,297. The Democrat had
2,554 first-place votes, and the Progressive incumbent had 2,982. Although the Democrat
was the Condorcet winner (a majority of voters preferred him in all two way contests), he
received the fewest first-place votes and so was eliminated. After the Democrat’s votes were
redistributed to the other two candidates, the Progressive won the election 4,314 to 4,067.
It was a very competitive election, as the winner’s margin of victory was 247 votes (2.8 %
of the electorate). A small shift in support from the Progressive to the Republican would have
resulted in a Republican victory. But what if Burlington’s electorate had been composed of
even more Progressive voters? If we shift the Progressive candidate up in 750 rankings, we
can construct the following election profile (Table 2, changes in bold).
Tab le 1 Ballot results from the 2009 Burlington, VT mayoral election (Laatu and Smith 2009)
Ranking 1513 495 1289 1332 767 455 2043 371 568
1st R RR D DDP P P
2nd DP P R DR
3rd P D R P R D
Each column represents a unique rank-order ballot cast by voters, and the top row denotes the number of vot-
ers who submitted that ballot. For instance, the first column denotes that 1513 voters ranked the Republican
first, the Democrat second, and the Progressive third. In the Burlington election, voters were permitted to sub-
mit incomplete rankings (a “truncated ballot”). Though this form of IRV is also susceptible to monotonicity
failure, for simplicity of analysis we do not include it in the model.
Public Choice (2014) 161:1–9 3
Tab le 2 Hypothetical ballot results for Burlington election
Ranking 1513 195 839 1332 767 455 2043 1121 568
1st R RRDDDP PP
2nd D PPR DR
3rd P DRP RD
As a result of this mass shift in voting, the first-place vote totals would nowbe: R—2,547,
D—2,554, and P—3,732. If the Progressive won the election in which those 750 voters
supported the Republican instead of him, then a monotonic voting system would award him
this election as well. However, in this hypothetical election, the Republican is eliminated
instead of the Democrat, and after redistributing the Republican’s votes, the Progressive
loses to the Democrat 3,927 to 4,067.
The Burlington election offers a compelling illustration of monotonicity failure’s prac-
tical importance, but such detailed IRV ballot data are rare. Therefore, in order to estimate
the frequency of its occurrence, we rely in this paper on a spatial model of elections. In the
following section, we describe the conditions under which a three-candidate election will
exhibit an upward monotonicity failure, which we use for the analysis of the model.1
3 Necessary and sufficient conditions for monotonicity failure
The outcome of any election conducted using Instant Runoff Voting can be represented by
a vector P, termed an election profile. Each element in Pis a non-negative integer denoting
the number of voters who cast a particular rank-ordered ballot. The sum of all elements in
Pis V, the number of voters. For three-candidate elections, we denote the candidates A,B,
and C,whereAis the IRV winner and Cis the candidate with the fewest first-place votes.
Therefore the elements in Pare a1,a
2,b
1,b
2,c
1,c
2as in Table 3.
An election profile Pexhibits an upward monotonicity failure if there exists a profile
Pthat is identical to Pexcept that candidate Ais ranked higher by a subset of voters, but
candidate Ais not the IRV winner. Formally, there must exist non-negative integers λ1and
λ2such that we can construct an election profile
P=a1+λ1+λ2,a
2,b
1λ1,b
2λ2,c
1,c
2
in which candidate Ais not a majority winner, candidate Bis eliminated, and candidate
Cis the IRV winner. According to our definitions from Sect. 1,prolePwill exhibit a
downward monotonicity failure. There are two conditions which, jointly, are necessary and
sufficient for the existence of P,shownin(1)and(2)below.
The first is that Pmust be a competitive election, defined as a profile in which2
c>V+2
4(1)
1Our analysis here closely parallels work by Lepelley et al. (1996) and Miller (2012), but differs in its con-
struction of condition (1). In our analysis of the spatial model (Sect. 4), we ignore cases where two candidates
tie for fewest first-place votes, so we include a stronger version of condition (1) than in these previous papers.
2For convenience, we define c=c1+c2.
4 Public Choice (2014) 161:1–9
Tab le 3 A three-candidate
election profile Ranking a1a2b1b2c1c2
1st choice A A B B C C
2nd choice B C A C A B
3rd choice C B C A B A
The second condition necessary for Pto exhibit an upward monotonicity failure is that
candidate Cmust be preferred over Aby a majority of voters. This implies that, absent a
tie, either candidate Cis the Condorcet winner, or that there is no Condorcet winner (the
election exhibits a majority cyclic triple). This condition can be expressed by:
c+b2>V
2(2)
The necessity of condition (1) follows from the requirement that candidate Acannot receive
a majority of first-place votes or tie under P. Formally
(b1λ1)+(b2λ2)+c>V
2(3)
Because we’ve also specified that candidate Bis eliminated under P, we can combine
(b1λ1)+(b2λ2)c1(4)
with (3), yielding equation (1).
The necessity of condition (2) follows from the requirement that candidate Cwins under
Pwith c+b2λ2votes. Since λ2is non-negative, it is necessary that Psatisfy (2).
To prove the sufficiency of conditions (1)and(2), we will show that when Psatisfies
(1)and(2), there must exist an election profile Pin which candidate Breceives fewer
first-place votes than C, and candidate Creceives a majority following Bs elimination.
Formally, it will suffice to show that under these conditions there exist non-negative integers
λ1and λ2that satisfy (4)and
c+b2λ2>V
2(5)
Let λ1=b1and λ2be the largest integer that satisfies (5). It follows by definition that
λ1is non-negative and from (2)thatλ2is non-negative. It follows by contradiction that
these values for λ1and λ2will also satisfy (4), because when (b2λ2)c,(1) implies
c+b2λ2>V+2
2,soλ2is not the largest integer satisfying (5). This completes the proof.
In the model presented in the following section, we use (1)and(2) to assess the mono-
tonicity failure rate of a set of simulated elections.
4 The model
The model we develop here is a two-dimensional spatial model, a method used widely to
analyze behavior in elections and performance among voting systems (Downs 1957; Merrill
1988; Kenny and Lotfinia 2005). Such modeling has also been used to inform disputes about
the merits of IRV in particular (Fraenkel and Grofman 2004; Horowitz 2004).
The positions of candidates and voters are represented by points on a two-dimensional
issue space, and each voter’s preference ranking is constructed by taking the reverse order
Public Choice (2014) 161:1–9 5
of the Euclidean distance to each candidate within the space.3Formally, let nrepresent the
number of issues (n=2 for this paper), let xji represent the ideal point for the jth voter’s ith
issue, and let yirepresent candidate y’s position on the ith issue. Voters rank each candidate
yin increasing order of utility, given by
uj(y) =n
i=1
(xji yi)21/2
(6)
Voters’ ideal points are randomly seeded across the issue space using one of four stylized
distributions. These distributions are not drawn from data, but are constructed to mirror
features from plausible real-world electorates. Such non-empirical distributions allow us to
gauge the model’s behavior over a wider range of scenarios than empirical data alone would
permit.
In the base case of the model, the ideal points on each axis are drawn from a Gaussian
distribution with mean 0 and standard deviation 0.25. In the “polarized” case, ideal points
are drawn at random from one of two bivariate Gaussian distributions, one centered at point
(0.25,0.25)and the other centered at (0.25,0.25), each with standard deviation 0.1.
This configuration mimics an election in which voters are split into two polarized camps. In
Sect. 5, we present the model results from two instantiations of this distribution: one where
voters are equally likely to be in either camp (Balanced Polarized), and one where voters
are 1.5 times more likely to position themselves in one camp than the other (Unbalanced
Polarized).
The final, “multiparty”, distribution randomly draws half of the voters’ ideal points from
the polarized distributions described above, one-quarter of the voters from distributions cen-
tered at (0.25,0.25)and (0.25,0.25), and one-quarter of the voters from a distribution
centered at (0.0,0.0). Each distribution has standard deviation 0.1. This configuration rep-
resents an election in which there are three major camps and two smaller camps. An illus-
tration of these three scenarios is in Fig. 1.
We model candidates as boundedly rational adaptive agents, following (Kollman et al.
1992; De Marchi 1999;Laver2005). Each candidate in the model attempts to maximize the
number of first-place votes received, but does not know his or her optimal location given
the locations of other candidates, and receives information only through periodic polling.
All three candidates begin the election at random positions in the voter distribution,4and
each period they determine how many first-place votes they would receive if the election
were held immediately. Candidates then change their positions on one or both issues by
a fixed increment if that adjustment would result in a higher first-place vote count. The
size of this fixed increment is 0.01, sufficiently small such that agents will not “overstep”
an advantageous position. The positions of voters do not change during the course of the
simulation.
Since outcomes are stochastic, we model 5,000 elections for each type of voter distribu-
tion (varying by the number of periods that candidates may move during each election, L).
Each election is parameterized with 1,001 voters, though outcomes are robust to halving
or doubling this value, or setting Veven or odd. The simulation code is available from the
authors on request.
3The qualitative results presented in this paper are robust to alternate specifications of utility, including city
block distance and squared Euclidean distance.
4In the polarized case, we ensure that there is at least one candidate in each “camp”, and two in the larger
camp.
6 Public Choice (2014) 161:1–9
Fig. 1 Examples of the three voter distributions utilized in the model. The balanced and unbalanced polarized
distributions are visually indistinguishable, and so only one case is illustrated here
5Results
The results from the model suggest that upward monotonicity failures are likely to occur
with significant frequency under IRV, and that this frequency increases with competitive-
ness. Depending on the type of voter distribution and length of the simulation, the simulated
elections exhibit monotonicity failure in anywhere from 0.7 % to 51 % of all cases, and
between 15 % and 51 % of competitive elections (excluding ties, which account for approx-
imately 1.1 % of simulated elections).
Monotonicity failure rates for each voter distribution appear to stabilize at higher values
of L(Fig. 2). The Unbalanced Polarized distribution exhibits the highest rate of monotonic-
ity failure (approximately 50 % at L>40), the Base Case and Balanced Polarized distribu-
tions exhibit monotonicity failures in 9 % to 12 % of simulated elections, and the Multiparty
distribution exhibits the most infrequent monotonicity failures (a lower bound of 0.7 %).
The simulation length parameter (L) appears to have a varied effect on the rate of mono-
tonicity failure. As Lincreases, the Base Case and Polarized distributions exhibit compet-
itive elections as defined by (1) more frequently, which in turn results in a higher overall
monotonicity failure rate. By contrast, the proportion of competitive elections tends to de-
crease in the Multiparty distribution as Lincreases, as illustrated by Fig. 3.
In the base case and polarized distributions, candidates will tend to settle on a local equi-
librium given enough time. In the base case, candidates position themselves near the yolk of
the distribution (McKelvey 1986) centered on (0,0). This central positioning increases the
chance of a three-way competitive election. Candidates in the two polarized distributions
tend to locate near the yolks of their respective camps. This invariably leads to a competitive
election in the Unbalanced Polarized case, where the two candidates in the larger camp each
take 30 % of the vote, but rarely results in a competitive election in the Balanced Polarized
case, where two candidates must split roughly 50 % of the vote between them. On average,
50 % of competitive elections in either polarized distribution result in the elimination of the
Condorcet winner, and therefore exhibit a monotonicity failure (Fig. 4).
By contrast, candidates in the Multiparty distribution never settle into a local equilibrium
near the yolk, regardless of simulation length. This is likely because candidates at the center
of the distribution who have captured the vote of one of the smaller peripheral camps have
an incentive to compete for one of the larger peripheral camps instead. This sets off a race
between two candidates to gain the support of the periphery, destabilizing the equilibrium
at the yolk, where elections are three-way competitive. As indicated by Figs. 3and 4,very
few elections conducted with the Multiparty voter distribution are competitive, but those
Public Choice (2014) 161:1–9 7
Fig. 2 Nonmonotonic rate (%) by simulation length (L). Values derived from 5,000 simulated elections for
each value of L(ties excluded)
Fig. 3 Percentage of elections that are competitive as a function of L. Values derived from 5,000 simulated
elections for each value of L(ties excluded)
Fig. 4 Nonmonotonic rate (%) of competitive elections by simulation length (L). Values derived from 5,000
simulated elections for each value of L(ties excluded)
8 Public Choice (2014) 161:1–9
Fig. 5 Nonmonotonic rate (%) of elections by competitive ratio. This chart is derived from 500,000 runs of
the simulation for each distribution. Each point illustrates the rate of monotonicity failure for elections with
competitive ratio between xand (x+0.05)
that are competitive exhibit monotonicity failure roughly 20 % of the time. Indeed, com-
petitive simulated elections exhibited montonicity failure at least 15 % of the time for all
parameterizations (Fig. 4).
In addition to reporting overall monotonicity failure rates, we investigate whether an
election’s degree of competitiveness has an effect on its monotonicity failure rate. To do
so, we construct 500,000 simulated elections for each voter distribution and plot the rate
of monotonicity failure as a function of an election’s competitive ratio (defined as the ra-
tio of first-place votes received by candidate Cto first-place votes received by candidate A;
elections with higher ratios are more competitive). Figure 5illustrates how the rate of mono-
tonicity failure increases with competitive ratio for all four voter distributions.
Finally, it is notable that very few of the model’s simulated profiles exhibited majority
cyclic triples. Of elections run with the Base Case distribution, only 0.4 % exhibited a major-
ity cyclic triple, 0.05 % in the Multiparty distribution, and 0.01 % for each of the Polarized
distributions. Since monotonicity failures can occur only when the election profile exhibits
a majority cyclic triple or when IRV fails to elect the Condorcet winner, this result indi-
cates that the monotonicity failures simulated here occur primarily due to IRV’s Condorcet
inefficiency in competitive elections.
6Conclusion
We have demonstrated here in a spatial model of voter behavior that upward monotonicity
failures arise in a non-trivial percentage of simulated elections. The lower bound estimate of
15 % in competitive elections represents a testable prediction of the model, and suggests that
three-way competitive races will exhibit unacceptably frequent monotonicity failures under
IRV. We also find that the rate of monotonicity failure increases with an election’s degree of
competitiveness, a finding that holds true for all of the distributions studied. We restrict our
attention in this paper to the three-candidate case for largely pragmatic reasons; the closed-
form method for determining which profiles exhibit monotonicity failure (Sect. 3) greatly
Public Choice (2014) 161:1–9 9
reduces the computational complexity of our model. The general case with more than three
candidates is a promising topic for future research.
Of course, upward monotonicity failure is not the only major defect of IRV, and future
work will need to examine the frequency of other paradoxes to which IRV is subject. Perhaps
the only definitive way these questions can be resolved is by examining a broad body of
data from real IRV elections. Such a body does not yet exist, though it is telling that out of
only two IRV elections in Burlington, VT, there has already been one recorded instance of
nonmonotonicity. If widespread use of Instant Runoff Voting continues, then we can expect
to see many more.
Acknowledgements The authors thank Ross A. Hammond and the anonymous reviewers for insightful
comments and suggestions. Any errors remain the responsibility of the authors.
References
Allard, C. (1996). Estimating the probability of monotonicity failure in a U.K. general election. Voting Mat-
ters,5, 1–7.
De Marchi, S. (1999). Adaptive models and electoral instability. Journal of Theoretical Politics,11(3), 393–
419.
Downs, A. (1957). An economic theory of democracy.NewYork:Harper.
Fishburn, P., & Brams, S. (1983). Paradoxes of preferential voting. Mathematics Magazine,56(4), 207–214.
Fraenkel, J., & Grofman, B. (2004). A neo-Downsian model of the alternative vote as a mechanism for
mitigating ethnic conflict in plural societies. Public Choice,121, 487–506.
Horowitz, D. L. (2004). The alternative vote and interethnic moderation: a reply to Fraenkel and Grofman.
Public Choice,121, 507–516.
Kenny, L. W., & Lotfinia, B. (2005). Evidence on the importance of spatial voting models in presidential
nominations and elections. Public Choice,123(3–4), 439–462.
Kollman, K., Miller, J., & Page, S. (1992). Adaptive parties in spatial elections. American Political Science
Review,86, 929–937.
Laatu, J., & Smith, W. (2009). The rank order votes in the 2009 Burlington mayoral election.http://
rangevoting.org/JLburl09.txt.
Laver, M. (2005). Policy and the dynamics of political competition. American Political Science Review,99(2),
263–281.
Lepelley, D., Chantreuil, F., & Berg, S. (1996). The likelihood of monotonicity paradoxes in run-off elections.
Mathematical Social Sciences,31, 133–146.
McKelvey, R. (1986). Covering, dominance, and institution-free properties of social choice. American Jour-
nal of Political Science,30(2), 283–314.
Miller, N. R. (2012). Monotonicity failure in IRV elections with three candidates. In World meeting of the
public choice societies, 2012.
Merrill, S. (1988). Making multicandidate elections more democratic. Princeton: Princeton University Press.
Norman, R. Z. (2006). Some properties of STV in close and polarized elections. In 2006 meeting of the
society for social choice and welfare.
Norman, R. Z. (2012). Frequency and severity of some STV paradoxes. In World meeting of the public choice
societies, 2012.
Smith, J. H. (1973). Aggregation of preferences with variable electorate. Econometrica,41, 1027–1041.
... More directly relevant are the results of Ornstein and Norman (2014), building on earlier work by Ornstein (2010). Analyzing simulated elections generated by various configurations of voter ideal points in a two-dimensional space with three candidates competing for first-preference support, they find that the resulting profiles are vulnerable to UMF 'in anywhere from 0.7 to 51% of all cases, and between 15 and 51% of competitive elections' (Ornstein and Norman 2014, p. 6) with the higher rates in the most competitive profiles. ...
... This paper has set out the precise conditions under which vulnerability to monotonicity failure arises in three-candidate IRV elections and has applied them to several large and varied sets of simulated ballot profiles in order to get a sense of the severity of IRV's monotonicity problems in varying circumstances. Confirming and extending the work of Ornstein and Norman (2014), it demonstrates that vulnerability to monotonicity failure should not be dismissed as a phenomenon that is logically possible but occurs very rarely. In particular, a substantial proportion of competitive IRV ballot profiles-and upwards of 50% of the most closely contested profiles-are vulnerable to monotonicity failure. ...
Article
Full-text available
A striking attribute of instant runoff voting (IRV) is that it is subject to monotonicity failure—that is, getting more (first-preference) votes may result in defeat for a candidate who would otherwise have won and getting fewer votes may result in victory for a candidate who otherwise would have lost. Proponents of IRV have argued that monotonicity failure, while a mathematical possibility, is highly unlikely to occur in practice. This paper specifies the precise conditions under which this phenomenon arises in three-candidate elections and applies them to a number of large simulated data sets in order to get a sense of the likelihood of IRV’s monotonicity problem in varying circumstances. The basic finding is that the problem is significant in many circumstances and very substantial when IRV elections are closely contested by three candidates.
... From a mathematical perspective, it is probably the most interesting ranked choice election in US history; that is, it was the most interesting until the 2021 Minneapolis, MN, election for the Ward 2 city council seat. In this article we explain what made the Burlington election so interesting and controversial (our information about this election comes from [1] and [4]), and explain why the Minneapolis election might be the new champion of ranked choice mathematical wackiness in the US. ...
... The raw vote data is available from www.preflib.org; this table appears in[4]. plurality winner of the election). ...
Preprint
In this article we explain why the November 2021 election for the Ward 2 city council seat in Minneapolis, MN, may be the mathematically most interesting ranked choice election in US history.
... The literature contains many critiques of transferable-vote elections. Fishburn (1983) explore a number of paradoxes of preferential voting; Woodall (1987) proves that certain desirable properties are logically incompatible in transferable-vote elections; Ornstein and Norman (2013) assess monotonicity failure in instant runoff voting, estimating that it surfaces in more than 15% of elections; and Miller (2017) refines that estimate for elections with three candidates. Another study relating to the specific question we address here finds that in four single-winner transferable-vote elections (mostly mayoral elections in the United States) the winner received less than a majority of the votes cast (Burnett and Kogan 2015). ...
Article
Full-text available
In ranked-choice elections, voters vote by indicating their preference orderings over the candidates. A ballot is truncated when the ordering is incomplete (called partial voting). Sometimes truncation is forced—voters are allowed to rank only a limited number of candidates—but sometimes it is voluntary. During the vote tabulating process, a truncated ballot is exhausted when all of the candidates it ranks have been eliminated. Ballot exhaustion and, therefore ballot truncation, is a concern in single-winner elections when the margin of victory in the final stage is less than the number of exhausted ballots. That concern motivates our study. We review evidence from actual single-winner ranked-choice elections and conclude that voluntary ballot truncation is very common. Moreover, it is difficult to explain strategically. To assess the significance of ballot truncation, we simulate ranked-choice elections with four, five and six candidates, using both spatial and random models of voter preferences. Does truncation change the probability that a Condorcet winner wins the election? Does the winner change as the extent of truncation increases? We find that even small amounts of truncation can alter election outcomes.
... This fact is repeated in most overviews of the mathematical properties of voting systems -papers such asNurmi (1983), or textbooks such asHodge and Klima (2005). 5 How much difficulty is not entirely clear;Ornstein and Norman (2014)'s model suggests non-monotonicity is common, especially in competitive elections. ...
Article
Full-text available
This paper geometrically compares multistage, multiple, and positional elections. The method of comparison shows that multiple stage elections are not necessarily more sensitive to small scale manipulation or other small scale effects. In particular, when all rank-order outcomes matter, multistage elections are in general less sensitive to perturbation, while in the case where the election’s outcome simply produces a singular winner and stages are not closely correlated, some multistage elections show similar or higher levels of intrinsic vulnerability to manipulation, error, and fraud as positional or multiple elections. In elections where the outcome simply produces a singular winner, a plurality vote is identified as less vulnerable in a single stage election than in multiple stages, while an antiplurality vote is identified as more vulnerable in a single stage than in multiple stages.
Article
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.
Article
The instant runoff voting (IRV) method fails the monotonicity criterion. This means in an IRV election it is theoretically possible for a winning candidate to lose an election if certain ballots are changed to raise the otherwise winning candidate higher on the ballot. We analysed data from over 100 real-world IRV elections to ascertain if any demonstrated a monotonicity anomaly. Despite theoretical research indicating potentially high incidence of such voting anomalies, our investigations found only one election showing a monotonicity anomaly: the 2009 Burlington mayoral election. Burlington was also the only election resulting in different winners using IRV, Borda Count, and Pairwise Comparison voting methods.
Article
en Ranked choice voting (RCV) is a voting system used commonly around the world, but only rarely in the United States. I present here a study that investigates how American voters act in an RCV election. Using a survey experiment design, I compare the election outcome and the behaviors and attitudes of voters in a plurality election to an RCV election. I find evidence suggesting RCV may not significantly change election outcomes and have no positive impact on voters’ confidence in elections and the democratic process. Study participants who voted in the RCV treatment were not any more likely to prefer RCV elections to plurality or majoritarian elections, and, overall, most voters do not prefer to vote in RCV elections and do not think that they result in fair election outcomes. Related Articles Boschler, Daniel. 2009. “Are Mixed Electoral System the Best Choice for Central and Eastern Europe or the Reason for Defective Party Systems?” Politics & Policy 37 (4): 735‐767. http://onlinelibrary.wiley.com/doi/10.1111/j.1747-1346.2009.00196.x/full Kim, Myunghee. 2007. “Citizens’ Confidence in Government, Parliament and Political Parties.” Politics & Policy 35 (3): 496‐521. http://onlinelibrary.wiley.com/doi/10.1111/j.1747-1346.2007.00070.x/full Berggren, Heidi M., Gregory A. Fugate, Robert R. Preuhs, and Dennis R. Still. 2004. “Satisfied? Institutional Determinants of Citizen Evaluations of Democracy.” Politics & Policy 32 (1): 72‐96. http://onlinelibrary.wiley.com/doi/10.1111/j.1747-1346.2004.tb00176.x/full Related Media Ranked Choice Voting Resource Center. n.d. http://www.rankedchoicevoting.org/ National Conference of State Legislators. 2017. “Ranked Choice Voting Has Its Red‐Carpet Moment in 2017.” March. http://www.ncsl.org/research/elections-and-campaigns/states-and-election-reform-the-canvass-march-2017.aspx Carrigan, Don, and Michael Kmack. 2017. “Maine Supreme Court Tackles Ranked Choice Voting.” April 13. http://www.wcsh6.com/news/politics/elections/maine-supreme-court-tackles-ranked-choice-voting/431027688 Raeburn, Paul. 2016. “How Election 2016 Would Be Different with Ranked‐Choice Voting.” October 17. http://www.newsweek.com/2016/10/28/election-2016-voting-science-510662.html Green, Nato. 2017. “Ranked‐Choice Voting a Barrier to Participation.” April 30. http://www.sfexaminer.com/ranked-choice-voting-barrier-participation/ Abstract es El voto por clasificación jerárquica (RCV por sus siglas en inglés) es un sistema de voto usado comúnmente alrededor del mundo, pero rara vez en los Estados Unidos. El presente estudio investiga cómo los votantes estadounidenses actúan en una elección de formato RCV. Usando un diseño de experimento de encuesta, comparo el resultado de la elección junto con el comportamiento y actitudes de los votantes en una elección plural contra una elección de RCV. Se encuentra evidencia que sugiere que RCV no cambia significativamente los resultados electorales, además de no tener ningún impacto positivo en la confianza de los votantes en las elecciones y en el proceso democrático. Los participantes del estudio que votaron en el diseño RCV no mostraron una mayor probabilidad a preferir las elecciones de RCV a las elecciones de pluralidad o mayoría, y en general la mayoría de los votantes no prefieren las elecciones de RCV y no creen que tengan resultados electorales justos. Abstract zh 优先选择投票(Ranked choice voting, 简称 RCV)是一种被全世界广泛使用的投票系统, 然而在美国却很少使用该系统。本文提出一项研究, 用以调查美国选民在RCV选举中的行为。通过设计一项调查实验, 将选举结果、选民对待相对多数选举制的行为和态度比作一场RCV选举。结果暗示:RCV可能并不会显著改变选举结果, 选民对选举以及民主过程的信心也不会因RCV而受到积极影响。与相对多数选举制或绝对多数选举制相比, 参与过RCV投票的调查对象表示将不会更青睐后者, 并且总体而言, 大多数选民不会更愿意参与RCV选举投票—他们认为该投票方式并不能得出公正的选举结果。
Article
Full-text available
A apatia política esta presente na sociedade brasileira que não participa ativamente das decisões políticas do Estado, potencializando os feitos negativos de agentes políticos em detrimento à essencialidade da política enquanto instrumento para o desenvolvimento social deste mesmo Estado. Neste matiz este estudo tem por objetivo trazer à lume a discussão sobre esta apatia e a justificativa da sua motivação. Quanto aos fins a pesquisa é exploratória e explicativa; e quanto aos meios, bibliográfica, documental e de observação teórico-empírica acerca da formação política do Estado. Como resultados foi possível constatar a latente apatia e a percepção/visão negativa da sociedade em relação à atividade política, fato corroborado pelos elevados índices de abstenção e votos brancos/nulos registrados nas eleições brasileiras, especialmente as quatro seguintes: 2008 (15% de abstenção e 17% de brancos/nulos); 2010 (18% de abstenção e 9% de brancos/nulos), 2012 (16% de abstenção e 19% de brancos/nulos) e 2014 (19% de abstenção e 10% de brancos/nulos). Palavras-chave: Política, Estado, Governo, Governabilidade.
Article
Full-text available
The political apathy is present in Brazilian society on those that does not participate actively in political decisions of the State, increasing the negative achievements of politicians instead policy essentiality as a tool for social development of the same State. In this sense, this study aims to underline the discussion of this apathy and the justification of its motivation. As to the purposes this research is exploratory and explanatory; and the means, bibliographical, documental and theoretic-empirical observation concerning political formation of the State. As results, it was possible to notice the latent apathy and perception/negative vision from society in relation to political activity, a fact corroborated by high levels of abstention and blank/null votes registered in Brazilian elections, especially the four: 2008 (15% abstention and 17% white/null); 2010 (18% abstention and 9% white/null), 2012 (16% abstention and 19% white/nul) and 2014 (19% abstention and 10% white/nul).
Article
Full-text available
The alternative vote (AV) is a preferential electoral system that tends to reward political moderation and compromise. Fraenkel and Grofman have modeled the likely effects of AV in severely divided societies, in order to impugn AV as a tool of interethnic accommodation. In this response, I show that Fraenkel and Grofman’s model is based on extreme assumptions that bear no relation to party and voter behavior in such societies. Models based on realistic assumptions about strategic behavior and cross-national experience with AV both demonstrate that AV generally provides centripetal incentives that can contribute to interethnic coalition-building and accommodation. Copyright Kluwer Academic Publishers 2004
Article
Full-text available
Among those advocating the use of particular electoralmechanisms to reduce the prospects for conflict and strengthendemocracy in societies that are deeply divided in ethnic orreligious terms, there are two main approaches, one associatedwith Arend Lijphart, one with Donald Horowitz. Lijphartadvocates using electoral rules such as list PR thatstrengthen the power of ethnically or religiously definedpolitical elites in the context of implementing power-sharingmechanisms at the elite level that institutionalize norms suchas proportional allocation and mutual veto across ethnies.Horowitz advocates using a preferential voting method, thealternative vote (AV), within constituencies thatare multi-ethnic in character, to allow for voting acrossethnic lines and to increase the likelihood of electingcandidates whose perceived obligations are wider than theirown ethnic group and/or to foster the creation of coalitionsthat are multi-ethnic in character. The main focus of thisessay is the reformulation of Horowitz’s approach in terms ofideas adapted from the neo-Downsian literature on median votermodels. We illustrate Horowitz’s approach with illustrationsinspired by the predominantly biracial political competitionin Fiji between native Fijians and those of Indian descent. Copyright Kluwer Academic Publishers 2004
Article
This paper proposes a model that takes the dynamic agent-based analysis of policy-driven party competition into a multiparty environment. In this, voters continually review party support and switch parties to increase their expectations; parties continually readapt policy positions to the shifting affiliations of voters. Different algorithms for party adaptation are explored, including "Aggregator" (adapt party policy to the ideal policy positions of party supporters), Hunter (repeat policy moves that were rewarded; otherwise make random moves), Predator (move party policy toward the policy position of the largest party), and "Sticker" (never change party policy). Strong trends in the behavior of parties using different methods of adaptation are explored. The model is then applied in a series of experiments to the dynamics of a real party system, described in a published opinion poll time series. This paper reports first steps toward endogenizing key features of the process, including the birth and death of parties, internal party decision rules, and voter ideal points.
Article
This book addresses a significant area of applied social-choice theory--the evaluation of voting procedures designed to select a single winner from a field of three or more candidates. Such procedures can differ strikingly in the election outcomes they produce, the opportunities for manipulation that they create, and the nature of the candidates--centrist or extremist--whom they advantage. The author uses computer simulations based on models of voting behavior and reconstructions of historical elections to assess the likelihood that each multicandidate voting system meets political objectives.Alternative procedures abound: the single-vote plurality method, ubiquitous in the United States, Canada, and Britain; runoff, used in certain primaries; the Borda count, based on rank scores submitted by each voter; approval voting, which permits each voter to support several candidates equally; and the Hare system of successive eliminations, to name a few. This work concludes that single-vote plurality is most often at odds with the majoritarian principle of Condorcet. Those methods most likely to choose the Condorcet candidate under sincere voting are generally the most vulnerable to manipulation. Approval voting and the Hare and runoff methods emerge from the analyses as the most reliable.Originally published in 1988.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Article
The spatial model of voting is a benchmark in theories purporting to explain political behavior. Underlying the spatial model is the assumption that both voters and candidates possess complete information. Despite the fact that much of the survey literature fails to confirm this assumption, few formal theorists have modeled electorates where the voters and candidates lack full information. In large part, spatial theory's failure to illuminate problems of this kind stems from its reliance upon an unrealistic model of human cognition: substantive rationality. This paper returns to Downs' original statement of the importance of information costs in voter decision-making, and extends Down's analysis to include the constraints faced by candidates. In this paper, complexity theory provides the framework to construct computational experiments that explore the use of information by political actors. As in real elections, voters have a finite amount of attention they dedicate to political issues, and candidates possess a fixed budget with which to poll the electorate. The inclusion of the costs of acquiring information for both voters and candidates results in a broader set of electoral outcomes that challenge current formal results.
Article
This paper proposes a model that takes the dynamic agent-based analysis of policy-driven party competition into a multiparty environment. In this, voters continually review party support and switch parties to increase their expectations; parties continually readapt policy positions to the shifting affiliations of voters. Different algorithms for party adaptation are explored, including “Aggregator” (adapt party policy to the ideal policy positions of party supporters), Hunter (repeat policy moves that were rewarded; otherwise make random moves), Predator (move party policy toward the policy position of the largest party), and “Sticker” (never change party policy). Strong trends in the behavior of parties using different methods of adaptation are explored. The model is then applied in a series of experiments to the dynamics of a real party system, described in a published opinion poll time series. This paper reports first steps toward endogenizing key features of the process, including the birth and death of parties, internal party decision rules, and voter ideal points.
Article
We develop a model of two-party spatial elections that departs from the standard model in three respects: parties' information about voters' preferences is limited to polls; parties can be either office-seeking or ideological; and parties are not perfect optimizers, that is, they are modelled as boundedly rational adaptive actors. We employ computer search algorithms to model the adaptive behavior of parties and show that three distinct search algorithms lead to similar results. Our findings suggest that convergence in spatial voting models is robust to variations in the intelligence of parties. We also find that an adaptive party in a complex issue space may not be able to defeat a well-positioned incumbent.
Article
ADA scores and Nominate scores are used for the first time to examine the influence of spatial voting records on which candidate wins the party’s presidential nomination and on which nominee wins the general election. We find that the most conservative Republican candidate and moderately liberal Democrats were most likely to win their party’s nomination. For general elections we find that the candidate’s spatial record has nearly as much impact on the outcome as economic growth, which has been the focus of most past empirical research. The nominee whose voting record is more moderate is more likely to be elected. Copyright Springer Science + Business Media, Inc. 2005