The Matching Hypothesis
Jeff Schank
PSC 120
Mating
• Mating is an evolutionary imperative
• Much of life is structured around securing and
maintaining long-term partnerships
Physical Attractiveness
• Focus on physical attractiveness may have
basis in “good genes” hypothesis
– Features associated with PA may be implicit
signals of genetic fitness
• Social Psychology: How does physical
attractiveness influence mate choice?
The Matching Paradox
• Assumption: Everybody wants the most attractive
mate
• BUT, couples tend to be similar in attractiveness
• r = .4 to .6 (Feingold, 1988; Little et al., 2006)
Matching Paradox
• How does this similarity between partners
come about?
• How is the observed population-level
regularity generated by the decentralized,
localized interactions of heterogeneous
autonomous individuals? (That’s a mouthful!)
Kalick and Hamilton (1986)
• Previously, many researchers assumed people
actively sought partners of equal
attractiveness (the “matching hypothesis”)
• Repeated studies showed no indication of this,
but rather a strong preference for the most
attractive potential partners
• ABM showed that matching could occur with a
preference for the most attractive potential
partners
The Model
• Male and female agents
– Only distinguishing feature is attractiveness
•
•
•
•
Randomly paired on “dates”
Choose whether to accept date as mate
Mutual acceptance  coupling
“Attractiveness” can represent any onedimensional measure of mate quality
The Model: Decision Rules
• Rule 1: Prefer the most attractive partner
• Rule 2: Prefer the most similar partner
• CT Rule: Agents become less “choosy” as they
have more unsuccessful dates
– Acceptance was certain after 50 dates.
The Model: Decision Rules more
Formally
( )
3
• Rule 1: Prefer the most attractive
Ap
partner
P1 =
1,000
• Rule 2: Prefer the most
similar partner
3
10 - Ao - Ap
• CT Rule: Agents become
P2 =
less “choosy” as they have
1,000
more
unsuccessful dates
(51-d )/ 50
c
(
– Acceptance was certain
after 50 dates.
Pi = ( Pi )
)
Model Details
• Male and Female agents (1,000 of each)
• Each agent randomly assigned an “attractiveness”
score, which is an integer between 1-10
• Each time step, each unmated male was paired
with a random unmated female for a “date”
• Each date accepted/rejected partner using
probabilistic decision rule
• If mutual acceptance, the pair was mated and left
the dating pool
Problem: Model not Parameterized
•
•
•
A )
(
P=
3

p
1
1,000
o
p
Pi = ( Pi )
(51-d )/ 50
kn

k- A -A )
(
P =

Pi = ( Pi )
3
1,000
c
p
1
10 - A - A )
(
P =
2
A )
(
P=
n
o
2
c
k
p
n
(D -d )/(D -1)
n
Model Parameterized
• Male and Female agent (1,000 of each) 
Nm (males) and Nf (females)
• Each agent randomly assigned an
“attractiveness” score, which is an integer
between 1 – 10  A random number
between 1 – Max(A)
What Can We Do?
• Replicate the model and check the original
results
– Are there any other interesting things to check
out?
• Modify the model
– Check robustness of findings
– Increase realism and see what happens
Replication
Rule 1
Rule 2
Kalick and Hamilton r
.55
.83
Mean r
.61
.83
95% Confidence Interval
(.57-.65)
(.78-.87)
95% confidence interval means 95% of simulations had results in this range.
Choice of Exponent n
• K & H used a 3rd-order power function with no
explanation
• What happens when we change the power?
Choice of Exponent n
1
Population Correlation
0.8
0.6
0.4
P1 =
Rule 1
0.2
Rule 2
P2 =
0
0
1
2
3
n
4
( )
Ap
10 n
(
10 - Ao - Ap
5
P3 =
n
10 n
P1 + P2
2
Pic = ( Pi )
(51-d )/ 50
)
n
Space and Movement
• Usually, agents are paired completely randomly
each turn
– Spatial structure can facilitate the evolution of
cooperation (Nowak & May, 1992; Aktipis, 2004)
– Foraging: Different movement strategies vary in
search efficiency and behave differently in various
environmental conditions (Bartumeus et al., 2005; Hills, 2006)
• Agents were placed on 200x200 grid (bounded)
allowing them to move probabilistically
• Could interact with neighbors only within a radius
of 5 spaces
Space and Movement
Zigzag
Brownian
Space and Movement
0.9
0.8
Population Correlation
0.7
0.6
0.5
Original
ZigZag
0.4
Brownian
0.3
0.2
0.1
0
Rule 1
Rule 2
Space and Movement
• Movement strategies and spatial structure
influence mate choice dynamics
• Population density should influence speed of
finding mates, as well as likelihood of finding an
optimal mate
• Suggests the evolution of strategies to increase
dating options (e.g., rise in Internet dating)
• Provides new opportunities for asking questions
about individual behavior and population
dynamics
Conclusions
• The Matching Paradox still remains
• There are parameter values for which either
rule can match the data
• Perhaps both rules are two simple
Mathematical Structure of Decision
Rules
• Qualitative difference easy to explain:
– Accept a mate with a probability that increases an
agent’s objective maximizing:
attractiveness (Rule 1) or similarity (Rule 2)
• There are many functions that could fit this
description
– Why a
power function?
– What is the probability of finding
a mate?
– Is this the same for each rule?
3rd-order
P1 =
P2 =
( )
Ap
3
10 3
(10 - A - A )
o
10
p
3
3
Mathematical Structure of Decision
Rules
A
B
0.35
0.3
Average Probability
Probability of Matching
0.3
0.25
0.2
0.15
0.1
0.2
0.1
Rule 1
0.05
Rule 2
0
1
2
3
4
5
6
7
8
9
0
10
Rule 1
Attractiveness
P1 =
(A )
p
10 3
3
P2 =
(
10 - Ao - Ap
10 3
)
3
Rule 2