ArticlePDF Available

Do Men and Women Have the Same Average Number of Lifetime Partners?

Authors:

Abstract and Figures

It is generally thought that for sake of consistency men and women must have the same average number of lifetime partners. However, this is not the case in general. When men have younger partners, women enter sexual relationships more quickly than men and have a higher number of lifetime partners. A male dominant model applied to UK data on the male rate of entry into a sexual relationship and the male partnership formation function shows that in a stationary population (zero growth rate) women have 9.1% more partners than men. In a stable population with an intrinsic growth rate of 2% and a larger but still plausible difference between the ages of partners, women have 24.6% more partners than men. Given that in sex surveys men report more partners than women, the resulting bias in estimated numbers of partners may therefore be larger than previously thought
Content may be subject to copyright.
PLEASE SCROLL DOWN FOR ARTICLE
This article was downloaded by:
[ARTZROUNI, MARC]
On:
5 November 2010
Access details:
Access Details: [subscription number 929143431]
Publisher
Routledge
Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-
41 Mortimer Street, London W1T 3JH, UK
Mathematical Population Studies
Publication details, including instructions for authors and subscription information:
http://www.informaworld.com/smpp/title~content=t713644738
Do Men and Women Have the Same Average Number of Lifetime
Partners?
MARC ARTZROUNIa; EVA DEUCHERTb
a Department of Mathematics, University of Pau, France b Swiss Institute for Empirical Economic
Research, University of St. Gallen, Switzerland
Online publication date: 05 November 2010
To cite this Article ARTZROUNI, MARC and DEUCHERT, EVA(2010) 'Do Men and Women Have the Same Average
Number of Lifetime Partners?', Mathematical Population Studies, 17: 4, 242 — 256
To link to this Article: DOI: 10.1080/08898480.2010.514853
URL: http://dx.doi.org/10.1080/08898480.2010.514853
Full terms and conditions of use: http://www.informaworld.com/terms-and-conditions-of-access.pdf
This article may be used for research, teaching and private study purposes. Any substantial or
systematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply or
distribution in any form to anyone is expressly forbidden.
The publisher does not give any warranty express or implied or make any representation that the contents
will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses
should be independently verified with primary sources. The publisher shall not be liable for any loss,
actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly
or indirectly in connection with or arising out of the use of this material.
Do Men and Women Have the Same Average
Number of Lifetime Partners?
Marc Artzrouni
Department of Mathematics, University of Pau, France
Eva Deuchert
Swiss Institute for Empirical Economic Research, University of
St. Gallen, Switzerland
It is generally thought that for sake of consistency men and women must have the
same average number of lifetime partners. However, this is not the case in general.
When men have younger partners, women enter sexual relationships more quickly
than men and have a higher number of lifetime partners. A male dominant model
applied to UK data on the male rate of entry into a sexual relationship and
the male partnership formation function shows that in a stationary population
(zero growth rate) women have 9.1%more partners than men. In a stable
population with an intrinsic growth rate of 2%and a larger but still plausible
difference between the ages of partners, women have 24.6%more partners than
men. Given that in sex surveys men report more partners than women, the result-
ing bias in estimated numbers of partners may therefore be larger than previously
thought.
Keywords: lifetime partners; male dominant model; stable population; stationary
population; United Kingdom
1. INTRODUCTION
To gain a better understanding of the dynamics of sexually trans-
mitted diseases, we rely on accurate data about sexual behavior. The
average number of lifetime sexual partners (LSPs) is a key parameter
(May and Anderson, 1992). Surveys of sexual behavior document
substantial discrepancies between men’s and women’s self-reported
numbers of LSPs (Buve
´et al., 2001; Laumann et al., 1994; Smith,
Address correspondence to Marc Artzrouni, Department of Mathematics, University
of Pau (BP 1155), 64013 Pau Cedex, France. E-mail: Marc.Artzrouni@univ-pau.fr
Mathematical Population Studies, 17:242–256, 2010
Copyright #Taylor & Francis Group, LLC
ISSN: 0889-8480 print=1547-724X online
DOI: 10.1080/08898480.2010.514853
242
Downloaded By: [ARTZROUNI, MARC] At: 12:07 5 November 2010
1992). Men and women report 10.8 and 6.2 partners, respectively, in
Quebec; 10.1 and 4.4 in France; and 11.5 and 5.0 in the United States
(Brisson et al., 1999). The UK’s National Survey of Sexual Attitudes
and Lifestyles II yields 12.7 lifetime partners for men and 6.5 for
women.
It is believed that this sex discrepancy is mathematically impossible
because with male and female populations of equal size, average num-
bers of LSPs should be the same for both sexes. Researchers have
ascribed this difference to various forms of response or sample selec-
tion bias which can result from misreporting or from sexual contacts
outside the sampled populations, notably with sex workers (Brown
and Sinclair, 1990; Catania, 1999; Brewer et al., 2000).
The equality of numbers of partners for men and women depends on
the definition. We will see that the numbers of entries into relation-
ship at one point in timeadded over all age groupsmust be the
same for both sexes. However, the average number of LSPs estimated
in sex surveys is the average over all ages aof the cumulated number
of relationships experienced up to age a. We show that when men
choose younger partners, the average number of LSPs is higher for
women than for men because women have an earlier sexual debut
than men.
In section 2 we discuss an illustrative example with two age groups.
We then use a continuous-time male dominant version of the model to
derive male and female average numbers of LSPs, which are consist-
ent but not necessarily equal. We give conditions under which the
female average will be greater than the male one. In section 3 we fit
male entry into relationship and male partnership functions to data
from the UK’s National Survey of Sexual Attitudes and Lifestyles II
(NATSAL II). In section 4 we discuss the implications of our results,
particularly with regard to the inconsistencies found in data on sexual
behavior.
2. MODEL
2.1. Two-Age-Group Example
We consider a stationary two-age-group population consisting of 200
young men and women and 100 old men and women (Figure 1). We
assume that men choose the total number of partners they desire
(male dominant model). Each young man chooses one woman, abbrevi-
ated as ‘‘pt’’ for partner. Each older man chooses two younger women
and one older one. The number of relationships experienced by an indi-
vidual of sex mduring the k-th period (m¼1 (women) or m¼2 (men))
Number of Lifetime Partners of Men and Women 243
Downloaded By: [ARTZROUNI, MARC] At: 12:07 5 November 2010
is k
m
(k). The numbers of partners chosen by young and old men are
k
2
(1) ¼1 and k
2
(2) ¼3. The imputed numbers of partners per woman
are k
1
(1) ¼(1 200 þ2100)=200 ¼2 and k
1
(2) ¼1. The average
number of entries into relationship at each period by men and women
is the same at 1.67.
If we let C
m
(k) be the cumulative number of partners of sex mup
to period k, then for men we have C
2
(1) ¼1 and C
2
(2) ¼4. This
means an average male number A
2
of LSPs equal to 2. The fact that
women have more partners when they are young than when they
are old translates into cumulative numbers in the first and second
age groups equal to C
1
(1) ¼2 and C
1
(2) ¼3, respectively. The female
average number of LSPs is equal to A
1
¼2.33, a figure that is 17%
higher than A
2
¼2 obtained for men. The higher figure for women
comes from the fact that women start accumulating partners at a
younger age.
In Figure 1, the fact that men choose younger partners was miti-
gated by the young age structure. If, however, both age groups have
200 individuals, then with other parameters remaining unchanged,
the imputed numbers of partners for women are 3 and 1 for the
two age groups instead of 2 and 1 previously. The relative scarcity of
young women means they have more partners and results in 2.5 and
3.5 LSPs for men and women, respectively. This translates into a
40%greater number for women.
FIGURE 1 Two-age-group example to illustrate the difference between male
and female numbers of sexual partners. Average numbers of partners during
one period are the same (1.67). The cumulated number of partners up to the
second age group is higher for men (4) than for women (3). The mean of the
lifetime numbers over the two periods is the mean number of lifetime sexual
partners (LSPs) estimated in sex surveys and is higher for women (2.33) than
for men (2).
244 M. Artzrouni and E. Deuchert
Downloaded By: [ARTZROUNI, MARC] At: 12:07 5 November 2010
This simple example shows that when men choose younger women,
women have more lifetime partners than men. In order to extend the
results to a realistic population, we describe a continuous-time version
of this model and prove a theoretical result when men always choose
younger partners.
2.2. Average Lifetime Number of Sexual Partners
We consider an age-structured two-sex population defined by female
and male densities N
k
(x) at age x(k¼1 for women, 2 for men). The
rates of entry into relationship are k
k
(x), k¼1, 2. This means that
individuals of sex kwhose age is in the interval (x,xþdx) establish
N
k
(x)k
k
(x)dx heterosexual partnerships. These partnerships can be
instantaneous with sex workers or repeated with lifetime partners.
The period lifetime number of sexual partners C
k
(a) for an individ-
ual of sex kand age ais the integral of k
k
(x)uptoagea:
CkðaÞ¼
def:Za
0
kkðxÞdx;k¼1;2:ð1Þ
The corresponding average numbers A
k
of LSPs in the population aged
between m
1
and m
2
are now:
Ak¼
def:Rm2
m1CkðsÞNkðsÞds
Rm2
m1NkðsÞds ¼Zm2
m1
ðRs
0kkðxÞdxÞNkðsÞds
Rm2
m1NkðsÞds ;k¼1;2:ð2Þ
2.3. Men/Women Consistency Condition
We postulate a male dominant model characterized by a male partner
acquisition function k
2
(x). We derive the male average number A
2
of
LSPs from Eq. (2). In order to calculate a consistent female average
number A
1
of LSPs, we first define the conditional probability density
function f
1
(uja) of the age uof a male partner given a woman’s age a
(‘‘female partnership formation function’’). Similarly, f
2
(aju) is the con-
ditional probability density function of the age aof a female partner
given a man’s age u(‘‘male partnership formation function’’). The fact
that the densities of new partnerships between women aged aand
men aged uare the same from the male and female perspectives
means that:
k1ðaÞN1ðaÞf1ðujaÞ¼k2ðuÞN2ðuÞf2ðajuÞ:ð3Þ
We bear in mind that f
1
(uja) and f
2
(aju) are density functions
(Rx
0f2ðajuÞda ¼1¼Rx
0f1ðujaÞdu where xis the maximum age in the
Number of Lifetime Partners of Men and Women 245
Downloaded By: [ARTZROUNI, MARC] At: 12:07 5 November 2010
population). We integrate both sides of Eq. (3) over uto obtain:
k1ðaÞN1ðaÞ¼Zx
0
k2ðuÞN2ðuÞf2ðajuÞdu:ð4Þ
The imputed female rate of entry into relationship is:
k1ðaÞ¼Rx
0k2ðuÞN2ðuÞf2ðajuÞdu
N1ðaÞ:ð5Þ
In order to calculate numbers of partners in a cohort, we assume
that male and female populations are stable. This means that both
populations have a constant age distribution and grow at the same
exponential rate. The densities N
2
(u) and N
1
(a) in Eq. (5) are then of
the form N
2
(u)exp(rt) and N
1
(a)exp(rt), where ris the intrinsic growth
rate and tis time. The male number A
2
of Eq. (2) and the imputed
female rate of entry into relationship k
1
(a) of Eq. (5) do not change over
time because exp(rt) cancels out in the numerator and the denomi-
nator. The cumulation
C1ðsÞ¼Za¼s
a¼0
k1ðaÞda ¼Za¼s
a¼0Rx
0k2ðuÞN2ðuÞf2ðajuÞdu
N1ðaÞda ð6Þ
is, for all female cohorts, the total number of relationships experienced
up to age s. We use this C
1
(s) to express the female total number of
LSPs of Eq. (2):
A1¼Rs¼m2
s¼m1Ra¼s
a¼0Rx
0k2ðuÞN2ðuÞf2ðajuÞdu
N1ðaÞda

N1ðsÞds
Rm2
m1N1ðsÞds :ð7Þ
This expression shows that a consistent female average number of
LSPs is expressed in terms of the male rate k
2
(u) and the male partner
formation function f
2
(aju). Moreover, integrating both sides of Eq. (4)
over ayields:
Zx
0
k1ðaÞN1ðaÞda ¼Zx
0
k2ðuÞN2ðuÞdu;ð8Þ
which shows that as required the total number of male and female new
relationships are equal. This is the common 1.67 of the introductory
two-age-group example. Also, Eq. (3) is satisfied with an imputed
female density f
1
(uja) equal to:
f1ðujaÞ¼
def:k2ðuÞN2ðuÞf2ðajuÞ
k1ðaÞN1ðaÞ¼k2ðuÞN2ðuÞf2ðajuÞ
Rx
0k2ðuÞN2ðuÞf2ðajuÞdu :ð9Þ
246 M. Artzrouni and E. Deuchert
Downloaded By: [ARTZROUNI, MARC] At: 12:07 5 November 2010
2.4. Theoretical Result
In the two-age group examples, men choosing younger women meant
that women had more LSPs than men (A
1
>A
2
). The role of the age
structure in this result is highlighted in Proposition 1, which provides
sufficient conditions for A
1
to be higher than A
2
.
Proposition 1. Under the assumptions:
.a
1
: the female and male population densities are equal on the
interval I ¼(m
1
,m
2
)(0, x): N
1
(x) ¼N
2
(x) for x 2I;
.a
2
: a man has no partner older than himself, or f
2
(aju) ¼0 for a >u
(therefore Ru
0f2ðajuÞda ¼1);
.a
3
: the populations during partnership formation years (ages u such
that k
2
(u) >0) are increasing functions of age: N
1
(u)=N
1
(a) >1 when
u>a,
we have A
1
>A
2
: the average number of LSPs calculated for ages
between m
1
and m
2
is higher for women than for men.
Proof. Eq. (2) shows that with equal male and female population den-
sities N
k
(x) for x2I(Assumption a
1
) the female average A
1
is greater
than the male average A
2
if C
1
(s)>C
2
(s) for any s2I. This means that
the total number of relationships up to age sis larger for women than
for men. To prove that C
1
(s)>C
2
(s):
C1ðsÞ¼Zs
0Rx
0k2ðuÞN2ðuÞf2ðajuÞdu
N1ðaÞda ðEq:ð6ÞÞ ð10Þ
¼Zs
0Rx
0k2ðuÞN1ðuÞf2ðajuÞdu
N1ðaÞda ða1:N2ðuÞ¼N1ðuÞÞ ð11Þ
¼Zx
0
k2ðuÞZs
0
N1ðuÞ
N1ðaÞf2ðajuÞda

du ðintegral exchangeÞð12Þ
>Zs
0
k2ðuÞZs
0
N1ðuÞ
N1ðaÞf2ðajuÞda

du ðutaken to sonlyÞð13Þ
¼Zs
0
k2ðuÞZu
0
N1ðuÞ
N1ðaÞf2ðajuÞda

du ða2;usÞð14Þ
>Zs
0
k2ðuÞZu
0
f2ðajuÞda

du ða3:N1ðuÞ=N1ðaÞ>1Þð15Þ
¼Zs
0
k2ðuÞdu ¼C2ðsÞða2:Zu
0
f2ðajuÞda ¼1Þ:ð16Þ
This shows that C
1
(s)>C
2
(s) and therefore A
1
>A
2
.
Number of Lifetime Partners of Men and Women 247
Downloaded By: [ARTZROUNI, MARC] At: 12:07 5 November 2010
Assumption a
1
is realistic because male and female population sizes
are usually close to each other until 50, an age at which the rate of
entries into relationship k
2
(u) becomes close to 0. Assumption a
2
takes
the male preference for younger partners to its extreme by assuming
that men never have an older partner.
Assumption a
3
states that the population is a decreasing function of
age at least during the partnership formation years, which can happen
in a stable population with a negative growth rate. These conditions
are sufficient to ensure that A
1
>A
2
. We will see in the numerical
applications that they are not necessary.
3. APPLICATION TO UK DATA
3.1. Background
We propose functional forms for the male parameters k
2
(u) and f
2
(aju).
These forms will be fitted to UK data and then used to obtain consist-
ent (but different) male and female averages A
1
and A
2
for a range of
scenarios concerning the growth rate of the population and the male
partnership function f
2
(aju). We will find that A
1
>A
2
in all cases even
though the conditions a
1
,a
2
, and a
3
of Proposition (1) are not always
satisfied: a
1
is only approximately true because male and female mor-
tality rates are slightly different; a
2
is not satisfied because the data
fitting will yield a density f
2
(aju) which does not drop to 0 for a>u
(some men have older partners); a
3
is not satisfied when the intrinsic
growth rate is positive (the population then decreases with age).
We use data from the UK’s National Survey of Sexual Attitudes and
Lifestyles II to estimate k
2
(u) and f
2
(aju). NATSAL II is a multistage
stratified random survey of 12,110 men and women (ages 16–44) who
were living in private households in Great Britain in 2000–2001. The
survey collected information on the total numbers of partners and
new partners over different time periods (during respondents lives,
the last five years, the last year, the last three months, and the last
four weeks). A detailed description of the survey design is in Erens
et al. (2001).
3.2. Male Rate k
2
(u) of Entry into Sexual Relationship
We model the cumulated number of partners C
2
(u) for men aged uas a
Gompertz-type function of the form
C2ðuÞ¼
def:p1expð expðp2ðup3ÞÞÞ;pk>0;k¼1;2;3;ð17Þ
248 M. Artzrouni and E. Deuchert
Downloaded By: [ARTZROUNI, MARC] At: 12:07 5 November 2010
where p¼(p
1
p
2
p
3
) is a vector of positive parameters: p
1
is the com-
pleted number of partners for u!1;p
2
is a measure of skewness,
and p
3
is the age at which k
2
(u) reaches its maximum. The derivative
of C
2
(u) is the male rate of entry into relationship:
k2ðuÞ¼
def:C0
2ðuÞ¼p1p2expðp2ðup3ÞÞexpðexpðp2ðup3ÞÞÞ:ð18Þ
We estimate the parameters using numbers of new partners in the
last year reported by men. Using Stata’s nonlinear least-square
routine we obtained the estimate:
^
pp ¼ð21:19 0:23 20:75Þ:
SE :ð0:90Þð0:02Þð0:24Þð19Þ
of p. Figure 2 shows that the resulting function k
2
(u) captures the
unimodal pattern in the male rate of entry into relationship, and the
rapid decline during the 20 s and 30 s.
3.3. Modeled Male Partnership Formation Function f
2
(aju)
We model f
2
(aju) as a three-parameter family of conditional Weibull
density functions of the form:
FIGURE 2 Reported average number of new partners during the last year, by
age uof man (grey bars) and corresponding fitted male partner acquisition
rate k
2
(u) of Eq. (18).
Number of Lifetime Partners of Men and Women 249
Downloaded By: [ARTZROUNI, MARC] At: 12:07 5 November 2010
f2ðajuÞ¼
0ifacðuÞ
aðuÞ
bðuÞ
acðuÞ
bðuÞ

aðuÞ1exp acðuÞ
bðuÞ

aðuÞ

if a>cðuÞ;
8
<
:
ð20Þ
where the shape, scale, and location parameters a(u), b(u), and c(u)are
functions of the man’s age u. This family of densities can be reparame-
terized in terms of any pair of age-specific low and high percentiles
P
L
(u) and P
H
(u) (with 0 <L<H<100) (Marks, 2005).
Given an age-specific location parameter c(u) (minimum age of
partner), the shape and scale parameters a(u) and b(u) of the density
in Eq. (20) are:
aðuÞ¼
ln lnð1H
100Þ
lnð1L
100Þ

ln PHðuÞcðuÞ
PLðuÞcðuÞ
 ð21Þ
and
bðuÞ¼PHðuÞcðuÞ
ln 1
1H
100

1=aðuÞ:ð22Þ
Because a quantile regression cannot be used to estimate the
zero-th percentile c(u) we approximate c(u) with the first percentile
P
1
(u). The NATSAL II datasets show that the first, 30th, and 70th per-
centiles P
1
(u), P
30
(u), and P
70
(u) are well approximated by linear func-
tions of the age uof the man (Figure 3). Using Stata’s quantile
regression routine to calculate the coefficients we obtain:
cðuÞ’P1ðuÞ¼12:38 þ0:12u
SE :ð1:40Þð0:06Þð23Þ
P30ðuÞ¼6:57 þ0:57u
SE :ð0:25Þð0:01Þð24Þ
P70ðuÞ¼2:76 þ0:88u
SE :ð0:36Þð0:01Þ:ð25Þ
Figure 4 represents the observed and fitted male densities f
2
(aju)of
Eq. (20) for three different ages of men. It shows a good fit for ages 20
and 30 for which the sample sizes were 228 and 127, respectively. For
age 40 there are only 46 men in the sample, which explains why the fit
is not that good.
250 M. Artzrouni and E. Deuchert
Downloaded By: [ARTZROUNI, MARC] At: 12:07 5 November 2010
In this baseline scenario the 0th, 30th, and 70th percentiles at age
15 are 14 years and 2 months, 15 years and 1 month, and 16 years.
This means that for a young man aged 15 the minimum age of his
FIGURE 4 Observed and fitted conditional density function f(aju) of the age a
of the partner for men aged u¼20, 30, 40.
FIGURE 3 Observed and fitted linear relationships between a man’s age and
the first, 30th and 70th percentile for the partner’s age (Eq. (23)–(25)).
Number of Lifetime Partners of Men and Women 251
Downloaded By: [ARTZROUNI, MARC] At: 12:07 5 November 2010
partners is 14 years and 2 months; 30%of his partners are under 15
years and 1 month; 70%of the partners are under 16. These three per-
centiles are 18 years and 5 months, 35 years, and 47 years and 9
months for men aged 50.
In order to assess the sensitivity of the average ages of partners we
will consider an ‘‘Alternative 20%lower age of female partner’’ scen-
ario. The 0th, 30th, and 70th percentiles 14 years and 2 months, 15
years and 1 month, and 16 years are the same as before. In addition
the three percentiles at age u¼50 are 20%lower than the values 18
years and 5 months, 35 years, and 47 years and 9 months obtained
for u¼50 in the baseline scenario. The linear equations become:
P1ðuÞ¼13:95 þ0:015u;P30ðuÞ¼9:58 þ0:37u;P70 ðuÞ¼6:77 þ0:61u:
ð26Þ
3.4. Average Numbers of Lifetime Sexual Partners
Stable female and male population densities N
k
(x,t) at age xand time t
are of the form:
N1ðx;tÞ¼berterx skðxÞ;N2ðx;tÞ¼SRB:berterxskðxÞ;ð27Þ
where bis a positive constant, rthe intrinsic growth rate, s
k
(x) the
probability of surviving to age xfor sex k; SRB, the sex ratio at birth,
is set to 1.05, the value most commonly found in human populations.
We use recent UK data for the female and male survival rates s
1
(x)
and s
2
(x). The averages A
k
are calculated between ages m
1
¼15 and
m
2
¼50. Cumulative numbers of partners C
k
(50) at 50 and averages
A
k
are calculated for six scenarios obtained by combining:
.three intrinsic growth rates requal to 2%,0%, and 2%. (The stable
populations with r¼0%are rough approximations of the structure
of the UK population in the mid 2000s.)
.the ‘‘Baseline’’ and the ‘‘Alternative 20%lower age of female part-
ner’’ scenarios described in Section 3.3.
The modeled male cumulative number of partners C
2
(x) as well as
the imputed female cumulative numbers of partners C
1
(x) (which
depend on the scenario and on the intrinsic growth rate) are shown
in Figure 5. The asymptotic values of these functions are the com-
pleted C
k
(50) given in Table 1. The numbers A
k
of LSPs in Table 1
are the integrals of the cumulative functions weighted by the popu-
lation structures [Eq. (2) and (7)].
252 M. Artzrouni and E. Deuchert
Downloaded By: [ARTZROUNI, MARC] At: 12:07 5 November 2010
Because of the male dominance men choose partners independently
of the age structure and scenario. This means in particular that the
completed number of partners C
2
(50) for men is the same (21.2) for
both scenarios and all intrinsic growth rates (Table 1).
TABLE 1 Sensitivity Analysis of Cumulated and Average Numbers of
Partners to Different Intrinsic Growth Rates for Two Scenarios Concerning
the Modeled Male Partnership Formation Function f
2
(aju)
Completed C
k
(50) Average A
k
Int. growth rate C
1
(50) C
2
(50) %diff. A
1
A
2
%diff.
1. Baseline UK partnership formation function
2%22.4 21.2 6.0 18.3 16.3 12.1
0%21.7 21.2 2.4 16.7 15.3 9.1
þ2%21.0 21.2 0.6 15.2 14.2 6.6
2. Alternative 20%lower age of female partner
2%23.4 21.2 10.4 20.3 16.3 24.6
0%21.7 21.2 2.5 18.1 15.3 18.4
þ2%20.2 21.2 4.3 16.2 14.2 13.6
Averages A
k
(k¼1, 2 for women, men, respectively) are calculated over the interval
(m
1
,m
2
)¼(15, 50).
FIGURE 5 Modeled male cumulative number of partners C
2
(x) (Eq. (17),
thick solid line) with imputed female cumulative numbers C
1
(x) for baseline
and alternative scenarios and three intrinsic growth rates, designated by
the thin lines.
Number of Lifetime Partners of Men and Women 253
Downloaded By: [ARTZROUNI, MARC] At: 12:07 5 November 2010
Figure 5 shows that, for both scenarios and all growth rates, women
accumulate partners more quickly than men do. As expected, the dif-
ference is accentuated with the Alternative scenario for which the age
difference is larger. In each scenario, the difference between men and
women is accentuated with the negative growth rate because the rela-
tively scarce young women in a declining population have more part-
ners (thick solid line for men versus two dashed lines for women
corresponding to the two scenarios).
When r¼0%and r¼2%then for both scenarios the added effect of
the partnership formation function and of the age structure results in
female functions C
1
(x) that remain larger than the male C
2
(x) for all x.
When r¼0%the female average number A
1
of LSPs is then 9.1%and
18.4%larger than the male value, for the Baseline and Alternative
scenarios, respectively. When r¼2%, the relative shortage of
younger women exacerbates the differences which reach 12.1%and
24.6%for the two scenarios (Table 1).
When r¼2%the female functions C
1
(x) remain smaller than the
male C
2
(x) except at the end of the period of sexual activity where
C
1
(50) is 21.0 and 20.2 for the Baseline and Alternative scenarios,
respectively. These numbers are slightly smaller than the male 21.2,
while the female average number A
1
of LSPs is 6.6%and 13.6%higher
than the male A
2
, for the Baseline and Alternative scenarios, respect-
ively. The younger age structure more than offsets the fact that the
cumulative male number of partners overtakes the female one at the
end of the period of sexual activity.
4. CONCLUSION
Reported data on numbers of LSPs obtained from the NATSAL II sur-
vey yield estimates of 12.7 and 6.5 partners for UK men and women
ages 15–45. Using only reported rates of partner acquisitions and a
stationary population, we obtained consistent baseline average num-
bers of LSPs equal to 15.3 and 16.7 for men and women, respectively
(Table 1). This 9.1%difference, applied to the reported male number
12.7, which is assumed accurate, translates into an average female
number of LSPs equal to 12.7 1.091 ¼13.9. The fact that this number
is higher than the male number of 12.7 makes the 6.5 partners
reported by women appear even more biased.
The reason for the discrepancy between the reported and imputed
female numbers is apparent if one compares the reported age specific
female rate of entry into relationship obtained from the NATSAL II
with the imputed (consistent) k
1
(x) of Eq. (5) (Figure 6, Baseline
254 M. Artzrouni and E. Deuchert
Downloaded By: [ARTZROUNI, MARC] At: 12:07 5 November 2010
scenario, r¼0). Figure 6 shows that if reports on men are accurate,
then women either underreport the number of partners they have
had in the last year or are not representative of the partners reported
by men. Sexual contacts with sex workers reported by men might not
be represented in the survey.
The NATSAL II data were also fitted to the female dominant ver-
sion of the model. The Weibull and Gompertz functions fit the data
for women on partnership formation and acquisition as well as it fits
the data for men (details not shown). With female data assumed accu-
rate, the same baseline scenario as above yields a female number of
6.5, which is equal to the reported number. The consistent male num-
ber of LSPs is 4.8. The fact that this number is smaller than the female
number of 6.5 makes the 17.3 partners reported by men appear even
more biased.
Although our model cannot reveal the origin of the men=women dis-
crepancy in reported numbers of LSPs, it demonstrates that claims on
the accuracy of the reported numbers should not be premised on a
theoretical men=women equality. In the common case of men having
younger partners, women have a higher number of LSPs than men.
The fact that women report fewer partners than men means that
the bias is more severe than previously thought and that more must
be done to understand its origin.
FIGURE 6 Reported (bars) and imputed (k
1
(x) of Eq. (5), solid line) rates of
entry into relationship for women. The fitted male rate of entry into relation-
ship plotted in Figure 2 is given in dotted lines.
Number of Lifetime Partners of Men and Women 255
Downloaded By: [ARTZROUNI, MARC] At: 12:07 5 November 2010
REFERENCES
Brewer, D., Potterat, J., Garrett, S., Muth, S., Roberts, J.J., Kasprzyk, D., et al. (2000).
Prostitution and the sex discrepancy in reported number of sexual partners. Pro-
ceedings of the National Academy of Sciences of the United States of America,
97(22): 12385–12388.
Brisson, M., Boily, M.-C., Ma
ˆsse, B.R., et al. (1999). Highlights of the sexual activity of
the heterosexual population in the province of Quebec. Sexually Transmitted
Infections,75: 296–299.
Brown, N. and Sinclair, R. (1999). Estimating number of lifetime sexual partners: Men
and women do it differently. The Journal of Sex Research,36: 292–297.
Buve
´, A., Lagarde, E., Carae
¨l, M., Rutenberg, N., Ferry, B., Glynn, J., et al. (2001).
Interpreting sexual behaviour data: Validity issues in the multicentre study on fac-
tors determining the differential spread of HIV in four African cities. AIDS,
15(Suppl 4): S117–S126.
Catania, J.A. (1999). A framework for conceptualizing reporting bias and its antecedents
in interviews assessing human sexuality. Journal of Sex Research,36: 25–38.
Erens, B., McManus, S., Field, J., Korovessis, C., Johnson, A., Fenton, K., et al. (2001).
National Survey of Sexual Attitudes and Lifestyles II: Technical Report. London:
National Centre for Social Research.
Laumann, E., Gagnon, J., Michael, R., and Michaels, S. (1994). The Social Organization
of Sexuality: Sexual Practices in the United States. Chicago: University of Chicago
Press.
Marks, N.B. (2005). Estimation of Weibull parameters from common percentiles. Jour-
nal of Applied Statistics,32(1): 17–24.
May, R. and Anderson, R. (1992). Infectious Diseases of Humans: Dynamics and Control.
Oxford: Clarendon Press.
Morris, M. (1993). Telling tails explain the discrepancy in sexual partner reports.
Nature,365(6445): 437–440.
Smith, T. (1992). Discrepancies between men and women in reporting number of sexual
partners: A summary from four countries. Social Biology,39(3–4): 203–211.
256 M. Artzrouni and E. Deuchert
Downloaded By: [ARTZROUNI, MARC] At: 12:07 5 November 2010
... Thus, assuming a closed population comprised of an equal number of men and women, the SP totals must balance across the sexes; therefore, the population means must be the same. And assuming an adequately sampled population of cooperative respondents who are capable of answering the SP question accurately, the mean of the solicited SP estimates should be the same for men and women and should provide a good approximation of the population mean (Dinkelman & Lam, 2009; also see Artzrouni & Deuchert, 2010). ...
... Thus, assuming a closed population comprised of an equal number of men and women, the SP totals must balance across the sexes; therefore, the population means must be the same. And assuming an adequately sampled population of cooperative respondents who are capable of answering the SP question accurately, the mean of the solicited SP estimates should be the same for men and women and should provide a good approximation of the population mean (Dinkelman & Lam, 2009; also see Artzrouni & Deuchert, 2010). ...
Chapter
Full-text available
The two surveys summarized in this chapter provide evidence consistent with two accounts of the partner discrepancy – the well-established finding that men report more opposite-sex sexual partners (SPs) than women (Laumann et al., 1994). Consistent with the strategies differences account (Brown & Sinclair, 1999), we found that: (a) people used a variety of strategies when responding to the SP question, (b) there was a strong relationship between the strategy selected and the magnitude of the response, (c) men were more likely than women to rely on rough approximation – a strategy associated with large SP estimates and overestimation, and (d) women were more likely than men to rely on conservative estimation strategies – in this case, providing many more small just-know responses than men. And consistent with the social desirability account, we found that: (e) the magnitude of the partner discrepancy depended on modality; as predicted, the discrepancy was larger when people were responding to interviewers over the telephone than when they were answering survey questions over the web. Interestingly the two accounts fit together nicely to explain the observed interaction between mode and sex. As it turned out, modality had no effect on SP estimates provided by the men whereas the web-based survey elicited larger estimates from women than did the telephone survey. This interaction was not driven by strategy selection; the pattern of strategy use displayed by the women was similar across modalities. Instead, we were able to pinpoint its cause in the responses provided by the women who used rough approximation. Specifically, SP estimates generated by these women were about twice as high when they were elicited anonymously over the web (M = 27.6) compared to when they were produced in response to a question delivered by a telephone interviewer (M =13.6). This finding is consistent with the general notion that social norms play a role in the partner discrepancy but suggests that their influence is more pronounced in some situations (e.g., for women, in the presence of another person, and in the absence of a preexisting tally or an easily enumerable set of SPs) than others.
Article
We apply a consistent sexual partnership formation model which hinges on the assumption that one gender's choices drives the process (male or female dominant model). The other gender's behavior is imputed. The model is fitted to UK sexual behavior data and applied to a simple incidence model of HSV-2. With a male dominant model (which assumes accurate male reports on numbers of partners) the modeled incidences of HSV-2 are 77% higher for men and 50% higher for women than with a female dominant model (which assumes accurate female reports). Although highly stylized, our simple incidence model sheds light on the inconsistent results one can obtain with misreported data on sexual activity and age preferences.
Article
Full-text available
On surveys, men report two to four times as many lifetime opposite‐sex sexual partners (SPs) as women. However, these estimates should be equivalent because each new sexual partner for a man is also a new sexual partner for a woman. The source of this discrepancy was investigated in this study. Participants reported number of lifetime and past‐year SPs and estimation strategies. The pattern of lifetime estimates replicated. The lifetime protocols indicated that people used different estimation strategies, that people who used the same strategy produced similar estimates, that some strategies were associated with large estimates and others with small ones, and that men were more likely to use the former and women the latter. No sex differences in estimates or strategies were apparent in the past‐year protocols. Our findings suggest that discrepant lifetime partner reports occur because men and women rely on different estimation strategies, not because they intentionally misrepresent their sexual histories.
Article
Full-text available
One of the most reliable and perplexing findings from surveys of sexual behavior is that men report substantially more sexual partners than women do. We use data from national sex surveys and studies of prostitutes and their clients in the United States to examine sampling bias as an explanation for this disparity. We find that prostitute women are underrepresented in the national surveys. Once their undersampling and very high numbers of sexual partners are factored in, the discrepancy disappears. Prostitution's role in the discrepancy is not readily apparent because men are reluctant to acknowledge that their reported partners include prostitutes.
Article
Full-text available
To describe and quantify the level of sexual activity of the heterosexually active population of Quebec. The data analysed included 2889 heterosexually active individuals aged 15-60 (agemed = 32) from a 1996-7 survey on the sexual lifestyles of the general population of Quebec. Various probability distributions were studied to assess their capacity to describe and quantify the lifetime and yearly numbers of sexual partners of the sampled population. To estimate the annual rates of new partner acquisition, a generalised linear model was fitted to the number of lifetime sexual partners as a function of age, years of sexual activity, and sex. The mean and variance of the number of lifetime sexual partners for men (mean = 11, s2 = 163) is higher than for women (mean = 6, s2 = 72). The negative binomial and lognormal probability distributions give the most adequate fit to the lifetime number of partners for both agglomerated and stratified (by sex and age) data. The estimated annual rates of new partner acquisition provide two important results for prevention: (1) the first year of sexual activity represents the highest annual rate of new partner acquisition independent of age, (2) annual rates of new partner acquisitions increase through mid-life (ages 40-50) combined with a decrease in condom use. Problems caused by the use of large categories in the estimation of mean and variance cannot totally be overcome by fitting probability distributions to the empirical data despite good fits. Furthermore, we believe that adequate estimates of the annual rate of new partner acquisition should be a better measure of the risk of HIV infection than the number of partners since the first is a measure of incidence while the second is a measure of prevalence.
Article
The present paper reviews conceptual models of self‐presentation bias in interview situations that focus on assessments of human sexuality. An heuristic framework is developed that synthesizes these models to focus on self‐presentation/self‐disclosure bias as a function of emotional distress and threat to self‐esteem, both intermediate outcomes that are influenced by four general factors: Respondent, Interviewer, Task, and Contextual. Empirical research within each of these four general factors is discussed, and areas for further research are outlined.
Article
The Social Organization of Sexuality reports the complete results of the nation's most comprehensive representative survey of sexual practices in the general adult population of the United States. This highly detailed portrait of sex in America and its social context and implications has established a new and original scientific orientation to the study of sexual behavior. "The most comprehensive U.S. sex survey ever." —USA Today "The findings from this survey, the first in decades to provide detailed insights about the sexual behavior of a representative sample of Americans, will have a profound impact on how policy makers tackle a number of pressing health problems." —Alison Bass, The Boston Globe "A fat, sophisticated, and sperm-freezingly serious volume. . . . This book is not in the business of giving us a good time. It is in the business of asking three thousand four hundred and thirty-two other people whether they had a good time, and exactly what they did to make it so good." —Anthony Lane, The New Yorker New York Times Book Review Notable Book of the Year
Article
Estimation of Weibull distribution shape and scale parameters is accomplished through use of symmetrically located percentiles from a sample. The process requires algebraic solution of two equations derived from the cumulative distribution function. Three alternatives examined are compared for precision and variability with maximum likelihood (MLE) and least squares (LS) estimators. The best percentile estimator (using the 10th and 90th) is inferior to MLE in variability and to one least squares estimator in accuracy and variability to a small degree. However, application of a correction factor related to sample size improves the percentile estimator substantially, making it more accurate than LS.
Article
Men and women in national surveys from four countries, the United States, Canada, Great Britain, and Norway, give mutually inconsistent reports of numbers of opposite-gender sexual partners. In all cases the number of female partners reported by men exceeds the number of male partners reported by women. Gender difference in reporting bias seems to be the most plausible explanation for the discrepancies. PIP It is extremely difficult to collect data on sexual behavior, because this behavior is considered private and intimate, it is connected to self-image and personality, and some sexual behaviors are illegal or taboo. In addition, researchers have scant experience in collecting these data, and even less methodological research has been done on optimal collection procedures. A comparison of surveys of the number of opposite gender sex partners reported by men and women can shed light on the reliability of these data. In a closed sample, these figures should be identical, so discrepancies indicate either deviation from the closed sample or inaccurate reporting. Examination of data from 5 US surveys and 1 each from Canada, the UK, and Norway provided an opportunity to consider possible adjustments and to discern a general pattern. The pattern which emerged from this study showed that men report more female partners than women report male partners. The ratio ranged from a low of 1.16:1 to 8.45:1, with discrepancies increasing as the reference period increased. Nonresponse levels were similar for men and women, and there is little evidence that this is linked to sexual behavior. The discrepancies are reduced by truncation, but this only produces small differences which are not necessarily more valid than raw data. The ratios are decreased when adjustments made for the gender distribution of the target population include the elderly, but they increase when the elderly are excluded. The possible explanations for the discrepancies are noncoverage, nonresponse, and misreports. Analysis points to intentional misreports as the most likely culprit, with men overreporting and women underreporting. Reference periods which include a greater portion of premarital life will likely be the most distorted. Until more methodological research isolates and minimizes measurement error, any analysis should assume that either the rates reported by men or those reported by women might be correct.
Article
An anomaly often noted in surveys of sexual behaviour is that the number of female sexual partners reported by men exceeds the number of male partners reported by women. This discrepancy is sometimes interpreted as evidence that surveys produce unreliable data due to sex-linked response and sampling bias. We report here that among the 90% of respondents reporting fewer than 20 lifetime partners, however, the ratio of male to female reports drops from 3.2:1 to 1.2:1. The anomaly thus appears to be driven by the upper tail of the contact distribution, an example of the general principle of outlier influence in data analysis. The implication is that sexual behaviour surveys provide reliable data in the main, and that simple improvements can increase precision in the upper tail to make these data more useful for modelling the spread of AIDS and other sexually transmitted diseases.