When to get married:
From individual mate search to
population marriage patterns
Peter M. Todd
Informatics, Cognitive Science, Psychology, IU
Center for Adaptive Behavior and Cognition,
Berlin
Overview of the talk
• The problem of sequential search
• Sequential search in mate choice
– One-sided search
– Mutual search
• Population-level (demographic)
implications and test
• Other sources of evidence
The problem of finding things
Search is required whenever resources are
distributed in space or time, e.g.:
• mates
• friends
• habitat
• food
• modern goods: houses, jobs, lightbulbs...
Another better option could always arrive, so
the real problem is:
when to stop search?
Choosing a mate
Mate choice involves:
1. Assessing relevant cues of mate quality
2. Processing cues into judgment of mate
quality
3. Searching a sequence of prospects and
courting on the basis of judged quality
Can be fast and frugal through limited cue
use (steps 1, 2), and limited search
among alternatives (step 3)
Features of mate search
No going back: once an alternative is passed,
there’s little chance of returning to it
No looking forward: upcoming range of
possible alternatives is largely unknown
How to decide when to stop?
A well-studied “mate search”
example: the Dowry Problem
A sultan gives his wise man this challenge:
• 100 women with unknown distribution of
dowries will be seen
• Women will pass by in sequence and announce
their dowry
• Search can be stopped at any time, but no
returning to earlier women
• Wise man must pick highest dowry or die
How can the wise man maximize his chances of
success and survival?
Fast and frugal search
Given a search situation with:
• Unknown distribution of alternatives
• No recall (returning to earlier options)
• No switching (once a choice is made)
then it can be appropriate to search using an
aspiration level, or satisfice (Simon, 1955)
Satisficing search
Satisficing search operates in two phases:
1. Search through first set of alternatives to
gather info and set aspiration level,
typically at highest value seen
2. Search through further alternatives and
stop when aspiration is exceeded
But how long to search in first phase for
setting the aspiration level?
Solving the Dowry Problem
Goal: Maximize chance of finding best option
Approach: Set aspiration level by sampling a
number of options that balances information
gathered against risk of missed opportunity
Solution: Sample N/e (= .368*N)
In other words, the 37% Rule...
The 37% Rule
Search through options in two phases:
Phase 1: Sample/assess first 37% of options,
and set aspiration level at highest value seen
Phase 2: Choose first option seen thereafter
that has a value above the aspiration level
Cognitive requirements are minimal:
remember one value and compare to it
An alternative criterion
Seeking the optimum takes a long time (mean
74% of population) and doesn’t often succeed
(mean 37% of times)
Instead, a more reasonable criterion: maximize
mean value of selected mates
This can be achieved with much less search:
check 9% of options instead of 37% in Phase 1
Take the Next Best rule: set aspiration after ~12
Maximizing mean value found
Mean mate value vs. phase1 search,
one-sided with no competition
100
Mean mate value selected
90
80
70
60
50
40
30
20
10
0
0
10
20
30
40
50
60
70
Length of phase1 search
80
90
100
More realistic mate search:
Mutual choice
Problem: Few of us are sultans
Implication:
• Mate choice is typically mutual
Empirical manifestations:
• most people find a mate...
• who is somewhat matched in
attractiveness and other qualities...
• after a reasonably short search
The Matching Game
• Divide a class in half, red and green
• Give each person in each half a number
from 1 to N on their forehead
• Tell people to pair up with the highest
opposite-color number they can get
Results:
• rapid pairing
• high correlation of values in each pair
Modeling mutual search
Kalick & Hamilton (1986): How does
matching of mate values occur?
Observed matching phenomenon need not
come from matching process:
• model agents seeking best possible mate
also produced value matching within
mated pairs
• however, they took much longer to find
mates than did agents seeking mates with
values near their own
Knowing one’s own value
Some knowledge of one’s own mate value
can speed up search
But how to determine one’s own value in a
fast and frugal way?
Answer: learn one’s own value during an
initial “dating” period and use this as
aspiration level, as in to Phase 1 of
satisficing search
Mutual search learning strategies
Methods for learning aspiration near own
mate value, decreasingly self-centered:
• Ignorant strategy: ignore own value and just
go for best (one-sided search)
• Vain strategy: adjust aspiration up with
every offer, down with every rejection
• Realistic strategy: adjust up with every
higher offer, down with lower rejections
• Clever strategy: adjust halfway up to every
higher offer, halfway down to lower rejects
Modeling mutual sequential
mate search
• Simulation with 100 males, 100 females
• Mate values 1-100, perceived only by other sex
• Each individual sequentially assesses the
opposite-sex population in two phases:
– Initial adolescent phase (making proposals/
rejections to set aspiration level)
– Choice phase (making real proposals/rejections)
• Mutual proposals during choice phase pair up
(mate) and are removed
How do different aspiration-setting rules
operate, using info of mate values and offers?
“Ignorant” aspiration-setting rule
Ignore proposals/rejections from others-just set aspiration level to highest value
see in adolescent phase
Equivalent to one-sided search rule used in
a two-sided search setting
Everyone quickly gets very high aspirations,
so few find mates...
Ignorant rule’s mating rate
Mean mated pairs vs. length of phase1 search,
ignorant mutual search rule
100
Mean number of mated pairs
90
80
70
60
50
40
30
20
10
0
0
10
20
30
40
50
60
70
Length of phase1 search
80
90
100
Ignorant rule’s matching ability
Mean within-pair mate value difference vs. length
of phase1 search, ignorant mutual search rule
20
Mean within-pair mate value
difference
18
16
14
12
10
8
6
4
2
0
0
10
20
30
40
50
60
70
Length of phase1 search
80
90
100
A better aspiration-setting rule
Idea: use other’s proposals/rejections as
indications of one’s own attractiveness,
and hence where one should aim
Adjust up/down rule:
For each proposal from more-attractive
individual, set aspiration up to their value
For each rejection from less-attractive
individual, set aspiration down to their
value
Adjust up/down rule’s mating rate
Mean mated pairs vs. length of phase1 search,
two mutual search rules
100
Mean number of mated pairs
90
Ignorant
80
Adjust up/down
70
60
50
40
30
20
10
0
0
10
20
30
40
50
60
70
Length of phase1 search
80
90
100
Adjust up/down rule’s matching
Mean within-pair mate value difference vs. length
of phase1 search, two mutual search rules
20
Mean within-pair mate value
difference
18
16
Ignorant
14
Adjust up/down
12
10
8
6
4
2
0
0
10
20
30
40
50
60
70
Le ngth of phase 1 se arch
80
90
100
Comparing search learning rules
Ignorant (one-sided) strategy forms
unfeasibly high aspiration levels and
consequently few mated pairs
Adjust up/down strategy learns reasonable
aspirations, so much of the population
finds others with similar values
(But still too few pairs are made, so other
strategies should be explored)
Summary so far—How others’
choices change mate search
Solo mate search: set aspiration to highest
value seen in small initial sample
[Add indirect competition: decrease size of
initial sample]
Add mutual choice: set aspiration using values
of proposers and rejecters in small sample
Testing search rules empirically
Difficult to observe individual sequential
mate search processes “in nature”
But we can see the population-level
outcomes of these individual processes:
the distribution of ages at which people
get married
Can we use this demographic data to
constrain our models?
Real age-at-marriage patterns
Age-specific conditional probabilities of first marriage
Age-specific conditional probabilities of first marriage
0.16
Prob(Marriage | Age)
Norway
Women, 1978
0.14
Romania
Men, 1998
0.12
0.10
0.08
Romania
Women, 1998 Norway
Men, 1978
0.06
0.04
0.02
Norway
Men, 1998
Norway
Women, 1998
0.00
18
23
28
33
38
Age at first marriage
43
48
Explaining age at marriage
Age-at-marriage patterns are surprisingly
stable across cultures and eras (Coale)
How to explain this regularity?
• Latent-state models: people pass through
states of differing marriageability
• Diffusion models: people “catch the
marriage bug” from other married people
around them (cf. networks)
Both can account for the observed data...
Psychologically plausible
accounts of age at marriage
...but neither latent-state nor diffusion
models are particularly psychological
Third type: search models
• from economics: unrealistic fully-rational
models with complete knowledge of
available partner distribution
• from psychology: bounded rational
models using more plausible satisficing
and aspiration-level-learning heuristics—
which ones will work?
One-sided searchers
Francisco Billari’s model (2000):
• Each individual searches their own set of
100 potential partners—one-sided, noncompetitive search
• Take the Next Best: assess 12, then take
next partner who’s above best of those 12
• Graph distribution of times taken to find
an acceptable partner (as hazard rate)...
Marriage pattern, one-sided model
Can one-sided search be fixed?
Monotonically-decreasing age-at-marriage
distribution is unrealistic
How can it be modified?
Billari introduced two types of variation in
learning period among individuals:
• positively age-skewed (unrealistic?)
• normally distributed around 12
Adding learning-time variability
Mutual search with learning
Previous model was unrealistic in being
one-sided (ignoring own mate value)
Does mutual search create the expected
population-level outcome?
• individuals start out with medium selfassessment and aspirations
• individuals learn using “clever” rule,
adjusting their aspiration partway up or
down to mate value of offerer or rejecter
Marriage pattern, mutual model 2
Fixing mutual learning search
Introducing mutual search with learning is
also not sufficient to produce realistic
distribution of ages at marriage
Again, adding variability in learning period
(normal distribution) works...
Adding learning-time variability
Real age-at-marriage patterns
Age-specific conditional probabilities of first marriage
0.16
Norway
Women, 1978
0.14
Romania
Men, 1998
0.12
0.10
0.08
Romania
Women, 1998 Norway
Men, 1978
0.06
0.04
0.02
Norway
Men, 1998
Norway
Women, 1998
0.00
18
23
28
33
38
43
48
Constraining search models
with population-level data
By comparing aggregate model outcomes with
observed population-level data, we found:
• one-sided search, mutual search, and aspiration
learning alone were not able to produce realistic
age-at-marriage patterns
• adding individual variation in learning/
adolescence times did produce realistic patterns
• other forms of variation (e.g., initial starting
aspiration, distribution of mate values) did not
help
Another empirical approach
Is there some way to observe the ongoing
mate choice process on an individual basis?
Mate choice in microcosm...
FastDating
®
How does FastDating work?
• ~20 men and ~20 women gather in one
room (after paying $30)
• Women sit at tables, men move in circle
• Each woman talks with each man for 5 min.
• Both mark a card saying whether they want
to meet the other ever again
• Men shift to the next woman and repeat
The rotation scheme
W1
W2
W3
W4
M1
M2
M3
M4
W1
W2
W3
W4
M4
M1
M2
M3
t
t+5
What happens next...
• Men’s/women’s “offers” are compared
• Every mutual offer gets notified by email,
with other’s contact info
• After that, it’s up to the pairs to decide
what to do….
What we can observe
Data we can get:
offers made and received
order in which people are met
matches made
--so (almost) like sequential search…
(except for some fore-knowledge of distribution,
and no control over when offers are actually made)
So next summer we’ll run our own session:
men and women kept separate, making decisions
immediately after each meeting, and giving us full
data about their traits and preferences
New mate search models
Individual variation in learning time is necessary
But is a fixed period of learning followed by
“real” search/offers very realistic?
Newer model with Jorge Simão produces
emergent variation:
• Search using aspiration levels
• Courtship occurs over extended period
• Maintain a network of contacts and switch to
better partners (if they agree)
Can look at marriage age vs. mate value,
distribution of ages, effect of sex ratio....
Age at marriage curves
Finding a parking place
One-sided parking search:
• Sequence of filled/empty spaces seen one
at a time
• Can’t tell what’s coming up
• Can’t turn around in the middle
Differences from one-sided mate search:
• Parking spaces get better as we go along
• Can turn around at very end
Driving/parking simulator
Conclusions
Sequential search heuristics use aspiration levels
set in simple ways to stop search, trading off
exploration against time/missed opportunities
People use such heuristics in some domains, and
may use them in mate choice
Populations of simulated individuals searching for
mates using simple search heuristics get married
at times corresponding to the distribution of
human marriages
Empirical data supporting search heuristic use at
the individual level is still needed (Fast-Dating)
For more information...
Todd, P.M., Billari, F.C., and Simão, J. (2005).
Aggregate age-at-marriage patterns from
individual mate-search heuristics. Demography,
42(3), 559-574.
Simão, J., and Todd, P.M. (2003). Emergent
patterns of mate choice in human populations.
Artificial Life, 9, 403-417.
Gigerenzer, Todd & the ABC Research Group
(1999). Simple Heuristics That Make Us Smart.
Oxford University Press.
Me: pmtodd@indiana.edu
The ABC group: www.mpib-berlin.mpg.de/abc
Searching with other goals
Maximizing chance of finding best option
requires using 37% Rule
But other adaptive goals can be satisfied
with less search:
Searching through about 10% of options in
phase 1 and then setting aspiration level
for further phase 2 search can produce
good behavior on several goals
Comparison of satisficing search
Making things harder
What happens when others join the search?
100 women searching through 100 men,
each seeking something different
This indirect competition forces faster
search...
Mate search with competition added
Mean mate value vs. phase1 search,
one-sided with and without competition
Mean mate value selected
100
90
No comp
80
Indirect comp
70
60
50
40
30
20
10
0
0
10
20
30
40
50
60
70
Length of phase1 search
80
90
100
Earlier models of marriage age
0.4
Piecewise-constant rates
0.3
Hernes
Log-logistic with immunity
Coale-McNeil
0.2
0.1
0.0
15
20
25
30
35
Age
40
45
50
New mate search models
Individual variation in learning time is necessary
But is a fixed period of learning followed by
“real” search/offers very realistic?
Newer model with Jorge Simão produces
emergent variation:
• Search using aspiration levels
• Courtship occurs over extended period
• Maintain a network of contacts and switch to
better partners (if they agree)
Can look at marriage age vs. mate value,
distribution of ages, effect of sex ratio....
Mating time related to quality
Mating time vs. sex ratio
(female/male sex ratio)
Mate quality vs. sex ratio
(female/male sex ratio)