The Matching Hypothesis

Jeff SchankPSC 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

• 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 one-

dimensional 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

• 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.

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

•

•

•

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 2Kalick 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.

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 3rd-order power function?– What is the probability of finding

a mate? – Is this the same for each rule?

Mathematical Structure of Decision Rules

1 2 3 4 5 6 7 8 9 10

-0.05

-4.16333634234434E-17

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Rule 1

Rule 2

Attractiveness

Pro

babi

lity

of M

atch

ing

Rule 1 Rule 2 Rule 30

0.1

0.2

0.3

Ave

rage

Pro

babi

lity

A B

Choice of Exponent n

• K & H used a 3rd-order power function with no explanation

• The assumption is that the exact nature of the function, including the value of the exponent, is unimportant

Choice of Exponent n

0 1 2 3 4 50

0.2

0.4

0.6

0.8

1

Rule 1

Rule 2

n

Pop

ulat

ion

Cor

rela

tion

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

Rule 1 Rule 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

OriginalZigZagBrownian

Pop

ulat

ion

Cor

rela

tion

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

• By modifying any number of the parameters, either decision rule can generate almost any desired correlation

• The Matching Paradox remains unresolved by Kalick and Hamilton’s (1986) ABM

• It is important to evaluate the effects of parameter values and environmental assumptions of a model