Content uploaded by Marc Artzrouni
Author content
All content in this area was uploaded by Marc Artzrouni on Jan 14, 2014
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 time—added over all age groups—must 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 expðp2ðup3ÞÞÞ;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
2ðuÞ¼p1p2expðp2ðup3ÞÞexpðexpðp2ðup3ÞÞÞ: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
aðuÞ1exp 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 PHðuÞcðuÞ
PLðuÞcðuÞ
ð21Þ
and
bðuÞ¼PHðuÞcðuÞ
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 r¼2%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 r¼2%, 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
