Euclidean Mate Value and Power of Choice on the Mating Market

Abstract

Three studies tested the hypothesis that human mate choice psychology uses a Euclidean algorithm to integrate mate preferences into estimates of mate value. In Study 1, a series of agent-based models identify a pattern of results relatively unique to mating markets where individuals high in Euclidean mate value experience greater power of choice: strong preference fulfillment overall and correlations between mate value and (a) preference fulfillment, (b) ideal standards, and (c) partner mate value. Studies 2 and 3 demonstrated that this pattern of results that emerges in human romantic relationships, is specific to mate value as a long-term partner, and is not accounted for by participant biases. These results suggest that human mate choice psychology uses a Euclidean algorithm to integrate mate preferences in mate choice, providing insight into the computational design of human mating psychology and validating this algorithm as a useful tool for future research.

Keywords

mate choice mate preferences assortative mating computer simulations evolutionary psychology

Mate selection is central to reproduction, the driving engine of biological evolution. This fact has motivated much research on human mate preferences, revealing universal preferences for kindness, intelligence, age, beauty, status, resources, health, and more (Buss, 1989; DeBruine, Jones, Crawford, Welling, & Little, 2010; Gangestad, Haselton, & Buss, 2006; Kenrick & Keefe, 1992; Singh, 1993). Despite this progress in understanding the content of mate preferences, mating research has generated less insight into how humans apply their preferences to select mates (Li & Meltzer, 2015). In particular, it remains unclear how people integrate information on multiple preferences into overall evaluations of their potential mates. Here, I test a hypothesis that humans select mates by integrating mate preferences according to a Euclidean algorithm. Specifically, I compare agent-based models with human samples to test the hypothesis that people who are more desirable according to Euclidean calculations experience greater power of choice on the mating market.

Mate preference integration is an essential step in mate choice. When selecting mates, all people face an array of imperfect potentials, each of whom will fulfill some preferences but not others. An intelligent mate may be unkind, a kind mate may be unhealthy, a healthy mate may be unattractive, and so on. Evaluating, comparing, and selecting among these imperfect potentials requires a psychology capable of combining information on each potential mate’s assets and blemishes into summary evaluations of their overall values as mates (Buss & Schmitt, 1993; Jonason, Garcia, Webster, Li, & Fisher, 2015; Jonason, Raulston, & Rotolo, 2012; Li, Bailey, Kenrick, & Linsenmeier, 2002).

Human mate choice psychology could use a variety of algorithms to accomplish this integration. A commonly assumed algorithm is a linear combination in which mate value is calculated as the sum of a potential mate’s trait values, weighted by the preferences for each of these values (Buss & Schmitt, 1993; Eastwick, Luchies, Finkel, & Hunt, 2014). Here, preferences act like slopes in a linear regression formula, with a stronger preference for a given trait manifesting as a stronger effect of that trait on overall mate value. Such linear combinations are powerful and intuitive but have many limitations. Chiefly, they cannot account for established nonlinear patterns of mate preference and attraction (Lee, Dubbs, Von Hippel, Brooks, & Zietsch, 2014; Li et al., 2002). For instance, men strongly prefer mates who are moderately physically attractive over mates who are physically unattractive, but do not discriminate as strongly between moderately and highly physically attractive partners (Li et al., 2002, 2013). Creating these nonlinear effects with a linear combination would require the addition of potentially intractable numbers of parameters. Curvilinear algorithms, using nonlinear functions such as sinusoidal functions, could account for these threshold effects more easily. Threshold effects could also emerge from categorical algorithms wherein mate preferences act as a series of hurdles which potential mates must pass (Miller & Todd, 1998; Todd, Billari, & Simão, 2005).

Alternatively, emerging evidence suggests a Euclidean algorithm is a good model for how human mate choice psychology integrates mate preferences. The Euclidean algorithm works by representing preferences and potential mates as points within an n-dimensional space, and computes mate value as proportional to the distance between these points (Conroy-Beam & Buss, 2016b). By computing a distance across dimensions, this Euclidean algorithm is able to compute an estimate of the mate value of a potential mate that simultaneously takes into account information across multiple preferences. Figure 1 presents a two-dimensional example. A person who ideally prefers their mate be very kind and intelligent (“P”) compares two potential mates: one who is moderately kind and moderately intelligent (“M1”) and one who is highly intelligent but highly unkind (“M2”). Mate M1 is closer to P’s mate preferences overall in this two-dimensional space and so their mate value to P is higher than M2’s.

Figure 1.

A two-dimensional representation of mate preference integration according to the Euclidean algorithm.

The Euclidean algorithm has many desirable features as an algorithm for integrating mate preferences. First, like linear combination or threshold algorithms, this Euclidean algorithm can integrate any number of preferences into a single summary mate value variable. Second, the Euclidean algorithm can account for threshold effects because it penalizes deviations from ideals in a noncompensatory fashion. Figure 1 illustrates this threshold effect. Mate M1’s mate value is 1.7 times greater than M2’s mate value even though M2 is more intelligent than M1. This mate value difference emerges because M2 is also very unkind. No amount of intelligence can compensate for M2’s large deficit in kindness. Whereas compensatory functions like linear combinations allow proximity to preferences on some dimensions to counterbalance deviations on others, the Euclidean algorithm generally creates natural thresholds: Large deviations from ideals on any one dimension strongly constrain mate value regardless of desirability on other dimensions.

Third, the Euclidean algorithm can account for interactions between preference dimensions without the addition of further parameters. Farrelly, Clemson, and Guthrie (2016) observed that perceived altruism and physical attractiveness interact to predict women’s attraction to potential mates: A man’s physical attractiveness increases his overall desirability more if he is also altruistic. Such an interaction is consistent with the Euclidean algorithm. Figure 1 illustrates this again: An increase in M2’s kindness would move M2 closer to P along a direct path, whereas an increase in M1’s kindness would move M1 closer to P only obliquely. An equivalent 1 unit increase in kindness would consequently increase M2’s mate value by 1.18 points but would only increase M1’s mate value by 0.75 points. With Euclidean integration, each preference dimension contributes more strongly to mate value in partners who are already desirable across several other dimensions.

In total, the Euclidean algorithm can integrate any number of preferences, strongly disfavors potential mates who are poor fits on any given preference dimension, and strongly favors partners who simultaneously fulfill multiple preferences. The algorithm consequently outperforms alternative algorithms in computer simulations of the evolution of mate choice (Conroy-Beam & Buss, 2016b), predicts features of human relationships (Conroy-Beam & Buss, 2016b), predicts attraction to potential mates better than a variety of alternative models (Conroy-Beam & Buss, 2017), and predicts feelings of satisfaction within long-term relationships (Conroy-Beam, Goetz, & Buss, 2016).

However, a critical prediction of the Euclidean integration hypothesis remains largely untested. If people actually integrate their preferences according to a Euclidean algorithm, the most desirable people on the mating market will tend to be those who fall closest to their potential mates’ preferences in the n-dimensional preference space—those who are highest in Euclidean mate value. By virtue of this desirability, these people should experience greater power of choice on the mating market. Although all people should fulfill their mate preferences reasonably well, those highest in Euclidean mate value should be most able to attract and pair with the mates they desire.

This power of choice could manifest in at least three ways. First, individuals higher in Euclidean mate value should better fulfill their preferences in mate choice because these individuals are most attractive to their preferred mates. Conroy-Beam and Buss (2016b) observed this relationship in agent-based models and human couples, but did not explore other manifestations of power of choice. For instance, if high mate value people have greater power of choice, these individuals can afford to set higher standards in mate choice and so should tend to set higher mate value ideals. Finally, if high mate value individuals both set higher standards and better fulfill their preferences, it follows that they should tend to pair with partners who are themselves higher in mate value: People should mate assortatively for Euclidean mate value.

Agent-based modeling provides a powerful method to test these predictions. Agent-based modeling is a computer modeling technique in which researchers simulate autonomous individuals, “agents,” who interact according to preprogrammed decision rules (Smith & Conrey, 2007). Using agent-based modeling, researchers can observe what system-level dynamics emerge when different psychologies drive individual-level behavior. Agent-based modeling has been used to explore mate choice patterns (Conroy-Beam & Buss, 2016a; Todd et al., 2005), including assortative mating (Kalick & Hamilton, 1986).

Here, I use agent-based models to examine the emergence and specificity of power of choice on the mating market. First, I construct simulated mating markets in which agents use a Euclidean algorithm to integrate their mate preferences. These simulated markets allow me to assess whether Euclidean mate preference integration does in fact afford agents high in Euclidean mate value greater power of choice on the mating market. Second, I construct a series of models to assess the specificity of this power of choice effect to markets driven by Euclidean integration relative to alternative markets. These alternative markets include markets wherein agents select their mates randomly or integrate their preferences using linear, curvilinear, or categorical algorithms. In addition, it is possible that people do not select their mates based on their preferences, but rather adjust their preferences to match their partners (Murray, Holmes, & Griffin, 1996). To assess whether such processes could create the appearance of power of choice, agents in one set of models select mates randomly but then change their preferences to better match the traits of their chosen partners. Finally, one series of models employs a reversed mating market in which agents high in Euclidean mate value have lower power of choice.

These several models serve as theory-building tools. If integrating mate preferences according to a Euclidean algorithm affords people high in Euclidean mate value greater power of choice on the mating market, evidence of this power of choice should emerge in simulated Euclidean mating markets but should not emerge with the same pattern or to the same degree in the alternative simulations. Furthermore, to the extent that human data correspond to this Euclidean simulation over alternative simulations, this suggests that human mate choice psychology uses a Euclidean algorithm to integrate preferences in mate choice.

In sum, if human mate choice psychology uses a Euclidean algorithm to integrate mate preferences, people who are higher in Euclidean mate value should tend to experience greater power of choice on the mating market. Because of this power of choice, a person’s Euclidean mate value should predict (a) the extent to which they fulfill their mate preferences, (b) the Euclidean mate value of their ideal partners, and (c) the Euclidean mate value of their chosen partners. Here, I test these predictions across three data sources. In Study 1, I construct an evolutionary agent-based model of mate choice based on Euclidean mate preference integration. This model shows that, in markets driven by Euclidean mate preference integration, individuals generally fulfill their mate preferences but Euclidean mate value evolves to predict mate preference fulfillment, ideal mate value, and partner mate value. In Studies 2 and 3, I test for these effects in two samples of human participants. If comparable patterns of relationships emerge in the human samples and Euclidean simulations, but not in alternative simulations, this suggests that human mate choice occurs in mating markets wherein Euclidean mate value affords greater power of choice because mate choice psychology uses a Euclidean algorithm to integrate mate preferences.

Study 1: Agent-Based Models of Mate Choice

In Study 1, I construct and analyze an evolutionary agent-based model of mate choice according to a Euclidean algorithm. This model allows me to observe the degree of mate preference fulfillment as well as the relationship between Euclidean mate value, mate preference fulfillment, ideal mate value, and partner mate value in mating markets where people high in Euclidean mate value have greater power of choice. Furthermore, to assess the extent to which these relationships are specific to Euclidean integration, I compare this primary model with a series of alternative models in which agents either use alternative mate preference integration algorithms or the mating market does not afford high mate value individuals greater power of choice.

Agent-Based Model

Agents

All models generated a population of 200 agents. Agents were randomly assigned to be either male or female. Each agent had 23 traits, drawn initially from random uniform distributions constrained to values between 1 and 7. Agents also had 23 preferences corresponding to each of these 23 traits. For the models testing alternative integration algorithms, each agent’s preference value was drawn from a random uniform distribution constrained to values between –10 and 10. For the models testing alternative mating market structures, agent preferences were drawn from random uniform distributions constrained between 1 and 7. Finally, all agents had an “energy” value used to determine their reproduction rate. At the start of each model run, the model selected a random optimum trait value between 1 and 7 for each of the 23 traits. For each agent, the model calculated the absolute deviation between each of the agent’s trait values and the optimum value for each trait. The amount of energy an agent earned from each trait was proportional to the deviation between the agent’s trait value and the optimum value.

Life cycle

Agents within the model followed a life cycle in which they computed their attraction to one another, selected each other as mates, reproduced with their chosen partners, and then died. This life cycle was repeated for 100 generations in each model run.

Computing attraction

In the primary model, agents computed their attraction to one another as the Euclidean distance between their preferences and the traits of each of their potential mates. Agents computed their attraction to all opposite-sex agents, yielding one matrix that represented how attracted all male agents were to all female agents and a second matrix that represented how attracted all female agents were to all male agents.

Mate selection

After computing attraction, the model began the mate selection phase. The model first produced a mutual attraction matrix by multiplying the male and female attraction matrices by one another. The resulting matrix represented how mutually attracted all possible agent couples would be. The model then identified the most mutually attracted agent couple, paired them, and removed them from the mutual attraction matrix. This process was iterated until all possible agent couples were formed. Agents who were left over after this pairing process died without reproducing. I also tested an alternative pairing process in which the model paired agents based on the smaller attraction value of each possible couple rather than the product of the agents’ attraction values; this pairing process did not produce qualitatively different results (see supplementary materials).

Reproduction

After pairing, agents reproduced with their chosen partners. The number of offspring produced by each agent couple was determined by the sum of the paired agents’ energy values. The model determined which agents reproduced in each generation by sampling with replacement from the agent couples. The model drew a sample of agent couples equal to the starting population size. The probability the reproduction procedure sampled a given agent couple was proportional to the sum of that couple’s energy values. This guaranteed a constant population size across generations but allowed the highest energy couples to produce the most offspring in each generation. For each offspring, the model randomly determined the offspring agent’s sex. The offspring then inherited their traits and preferences from their parents. For each trait or preference, offspring randomly inherited the corresponding value of either their male or female parent. The model then added a small amount of random normal noise to this random value to simulate mutation; this noise was centered on M = 0 and had a standard deviation of 0.06, or 1% of the total trait range. Offspring energy values were then determined as the deviation of their resulting trait values from the previously determined optimum values for that model.

Death

Finally, after reproduction, all parent agents were replaced by their offspring. Offspring agents then became the parent agents for the next iteration of the cycle.

Model manipulations

To assess the specificity of the Euclidean effects analyzed in the primary model, I also analyzed seven alternative versions of this primary model: the aspiration, linear, curvilinear, cosine similarity, random, preference-updating, and reversed market models.

Agents in the first four alternative versions integrated their preferences using algorithms other than the Euclidean algorithm. Agents in the aspirational model integrated their preferences using an algorithm inspired by Miller and Todd (1998). These agents evolved preferences that specified an ideal range for each trait; an agent passed an aspiration check if their trait value fell inside this ideal range but failed if not. Aspiration agents calculated their attraction to potential mates as the number of aspiration checks each potential mate passed. Agents in the linear model evolved preferences that acted like slopes and intercepts in a multiple regression-like formula. Agents in this model computed their attraction to potential mates as the sum of their traits multiplied by the agent’s preference values, plus an intercept term. Curvilinear agents evolved preferences that acted as slopes in a sinusoidal function. These preferences manipulated the phase and frequency of the resulting sine wave, allowing these agents to evolve attraction functions with multiple shapes ranging from straight lines to complex curves.

Agents in the cosine similarity model calculated their attraction to potential mates using a similarity metric similar to the Euclidean distance. Cosine similarity integration, like Euclidean integration, treats preferences and potential mates as points in an n-dimensional space. However, rather than computing the distance between these points, cosine similarity computes the cosine of the angle formed between the two points and the origin. Cosine similarity integration thus does not find potential mates whose traits are necessarily identical to ideal preferences, but rather finds mates whose traits are oriented similarly to preferences with respect to the origin in preference space. This metric is commonly used in text mining applications to assess the similarity of documents, which may be very different in length (Huang, 2008).

The remaining three models used Euclidean mate preference integration but tested alternative possible mating market structures. The random and preference-updating models did not use agent preferences to guide mate choice. Agents in the random model integrated their preferences into attraction values using a Euclidean algorithm but selected mates randomly with respect to attraction. Agents in the preference-updating model also selected mates randomly with respect to their mate preferences. However, after mate selection, these agents also adjusted their mate preferences such that they were 50% closer to the traits of the partner they had already chosen. These agents thus do not use their preferences to select their partners, but rather select their preferences to fit their chosen mates.

Finally, agents in the reversed market model computed their attraction to one another using Euclidean mate preference integration. However, during the mate selection phase of the life cycle, the reversed market model paired agents with the largest differences in their attraction values. This market tends to give the people lowest in Euclidean mate value greater power of choice because they will tend to be highly attracted to their preferred partners but will not tend to be highly attractive to these partners in return.

Model analysis

I ran each agent-based model a total of 100 times. Within each model run, I calculated three primary variables in the final agent generation: (a) Euclidean mate preference fulfillment, (b) the Euclidean mate value of each agent, and (c) the Euclidean mate value of each agent’s ideal partner. Mate preference fulfillment was calculated as the Euclidean distance between each agent’s preferences and the traits of their chosen partner. This distance was scaled and transformed to a percentage of maximum possible (POMP) metric such that a value of 1 indicated the agent’s mate perfectly fulfilled their preferences and a value of 0 indicated that the agent’s mate was the maximum possible distance from their preferences. For aspirational agents, mate preferences were defined as the central value of each of the agent’s ideal ranges; for liner and curvilinear agents, mate preferences were defined as the value for each trait that the agent found most attractive.

Agent Euclidean mate value was the transformed Euclidean distance between each agent’s own traits and the average preferences of the opposite sex; a value of 10 indicated the agent perfectly fulfilled the opposite sex’s average preferences, a value of 0 indicated minimum possible mate value. Finally, the mate value of each agent’s ideal partner was calculated as the transformed Euclidean distance between that agent’s preferences and the average preferences of the agent’s own sex. This distance also ranged from 0 to 10 and reflected the extent to which the agent pursued partners that were highest in mate value to their own sex.

At the end of each model run, I calculated within the final population the agents’ average mate preference fulfillment and three correlations. The first correlation was between each agent’s mate value and the extent to which the agent’s mate fulfilled their mate preferences. The second correlation was between each agent’s own mate value and the mate value of their ideal partner. Finally, I calculated assortative mating for mate value as the correlation between each female agent’s mate value and the mate value of her male partner. I stored the values of each of these effects within each model run and report the average effect across model runs with 95% confidence intervals (CIs) based on the variability in these effects across model runs.

Results

Figure 2 shows the correlation results of the primary, Euclidean model of mate choice. Across model runs, agents in general selected mates very close to their preferences in preference space: M = 0.76, 95% CI = [0.75, 0.77]. Nonetheless, agents high in Euclidean mate value showed evidence of having more power of choice on the mating market. These individuals fulfilled their mate preferences better, r_mean = .39, 95% CI = [0.36, 0.42], tended to evolve higher mate value ideals, r_mean = .48, 95% CI = [0.44, 0.52], and paired with higher mate value partners, r_mean = .63, 95% CI = [0.60, 0.65].

Figure 2.

Correlation results from the primary, Euclidean agent-based model.

In addition, Figure 3 shows that this pattern of results is relatively specific to mating markets based on Euclidean mate preference integration. Only the preference-updating model produced average preference fulfillment values that approached the Euclidean model, but this model did not produce any of the correlation effects indicative of greater power of choice for agents with higher mate value. The linear and cosine similarity models were able to produce power of choice correlations in the same direction as the Euclidean model. However, these correlations were weaker than those observed in the Euclidean model and neither model produced Euclidean preference fulfillment close to the Euclidean model or even substantially better than the random model.

Figure 3.

The pattern of results produced by each of the eight agent-based models.

The random model produced neither strong mate preference fulfillment nor power of choice correlations that were significantly different from zero. Finally, the reversed market produced mate preference fulfillment weaker than that found in the Euclidean model and negative correlations between agent mate value and preference fulfillment as well as for assortative mating for mate value. This model, additionally, produced a significant and positive but weak correlation between agent mate value and ideal partner mate value. Model scripts and plots of all effects can be found in the supplementary materials.

Discussion

Overall, Study 1 demonstrated a pattern of effects that is relatively diagnostic of Euclidean mate preference integration. In mating markets driven by Euclidean mate preference integration, individuals in general strongly fulfilled their mate preferences with average preference fulfillment near 75% of maximum. Furthermore, individuals high in Euclidean mate value experienced greater power of choice, and Euclidean mate value evolved to predict (a) mate preference fulfillment, (b) the mate value of ideal partners, and (c) the mate value of chosen partners. This pattern of effects does not clearly emerge in random mating markets, markets in which agents use alternative preference integration algorithms, markets in which agents match their preferences to their chosen partners, or in markets where agents low in Euclidean mate value experience greater power of choice. This diagnostic pattern of effects, therefore, emerges in, and is specific to, mating markets in which mate preferences are integrating according to a Euclidean algorithm. The emergence of this pattern of effects in human samples would suggest that human mate selection psychology uses a Euclidean algorithm to integrate mate preferences in mate choice.

Study 2: Euclidean Mate Value and Power of Choice in an Online Sample

In Study 2, I use a sample of human participants to assess whether the diagnostic pattern of results demonstrated in Study 1 emerges in human romantic relationships. Participants reported their ideal mate preferences and rated themselves and their partners on the same dimensions. If the pattern of results documented in Study 1 emerges in human romantic relationships, this suggests that Euclidean mate value, in fact, affords greater power of choice on the mating market because people integrate their preferences according to a Euclidean algorithm.

Furthermore, because participants are engaged in committed, romantic relationships—presumably formed on a long-term mating market—I examine the specificity of these effects to long-term mate value. People express different preferences for long- and short-term mates (Kenrick, Sadalla, Groth, & Trost, 1990), and so, the same person’s mate value as a long-term mate can differ from their mate value as a short-term mate. If human mate choice psychology uses a Euclidean algorithm to integrate long-term preferences, power of choice on the long-term mating market should emerge from a person’s long-term Euclidean mate value and not from their short-term Euclidean mate value. This power should further apply only to long-term mating outcomes: People’s long-term mates should better fulfill their long-term preferences than their short-term preferences and people high in long-term Euclidean mate value should not tend to better fulfill their short-term preferences, set higher ideals for a short-term partner, or pair with partners higher in short-term mate value. The pattern of diagnostic effects documented in Study 1 should be specific to participant’s long-term mate value and should not independently emerge for participant’s short-term mate value.

Method

Participants

Participants were 246 people (143 female) in committed, long-term, heterosexual relationships recruited from Amazon’s Mechanical Turk. Participants came from a larger sample of n = 319; 73 participants were excluded from all analyses because they failed at least one of two attention check items. Participant recruitment was targeted at a final sample size of n = 250, which power analysis indicated would yield power of at least 80% for all relevant effects. Participants were M = 34.35 years old on average, SD = 9.98, and the median relationship length in this sample was Mdn = 60 months.

Measures

All participants reported their ideal mate preferences using a 23-item bipolar adjective instrument. Each item in this instrument had seven points ranging from, for example, very unkind to very kind. Participants were asked to report their ideal trait value for each of the 23 traits in an ideal long-term partner, defined as a “committed, romantic relationship,” as well as an ideal short-term partner, defined as a “one-night stand; uncommitted, sexual relationship.” The scale was the same scale used in Conroy-Beam et al. (2016). Participants used the same scale to provide ratings of themselves on each of the 23 dimensions as well as ratings of their actual long-term partner. Participants completed all ratings in random order.

Analyses

I used the ideal, self, and partner ratings to compute eight values for each participant: mate preference fulfillment, participant mate value, partner mate value, and ideal mate value for both long- and short-term relationships.

Mate preference fulfillment

The first two values calculated for all participants were each participant’s long-term and short-term mate preference fulfillment: the extent to which the participant’s actual partner fulfilled their long- and short-term preferences. This was computed as the Euclidean distance between the participant’s ideal preferences and their partner’s traits, transformed such that a value of 1 indicated maximum mate preference fulfillment.

Self, ideal, and partner mate value

For each participant, I also calculated the participant’s long- and short-term mate value as well as the short- and long-term mate values of their actual partners and their ideal partners. These were calculated as the Euclidean distance between (a) the participant’s own traits and the opposite sex’s average preferences for participant mate value, (b) partner traits and the average preferences of the participant’s own sex for partner mate value, and (c) the traits of the participant’s ideal partner and the average preferences of the participant’s sex for ideal mate value. These Euclidean distances were transformed such that a value of 10 indicated maximum mate value.

Results

Figure 4 shows the zero-order relationships between participant’s long-term Euclidean mate value and long-term mate preference fulfillment, ideal long-term partner mate value, and long-term partner mate value. Participants strongly fulfilled their long-term mate preferences overall, M = 0.79, 95% CI = [0.77, 0.80]. Yet, participants who were higher in long-term Euclidean mate value more strongly fulfilled their ideal long-term mate preferences, r(244) = .35, p < .001. These participants also tended to set higher standards in that they had ideal partners with higher mate value, r(244) = .56, p < .001. Finally, participants mated assortatively for long-term Euclidean mate value: high mate value participants tended to be mated to high mate value partners, r(244) = .54, p < .001.

Figure 4.

Power of choice relationships from Study 2.

Figure 5 compares these effects with the pattern of effects produced by each of the eight agent-based models from Study 1. I calculated the similarity between Study 2’s effects and the effects produced by each run of the eight agent-based models using three common similarity metrics: the Euclidean distance, the Manhattan distance, and cosine similarity. Each similarity metric was transformed such that higher values indicated greater similarity and converted to a POMP metric. The Euclidean model was most similar to Study 2 according to all three similarity metrics.

Figure 5.

Similarity between the pattern of effects produced in Study 2 and the eight agent-based models from Study 1.

In addition, these results were specific to long-term relationships. Participants more strongly fulfilled their ideal long-term preferences (M = 0.79, 95% CI = [0.77, 0.80]) than their ideal short-term preferences (M = 0.71, 95% CI = [0.70, 0.73]), t(244) = 9.90, p < .001, Cohen’s d = 0.63. Furthermore, participant’s long-term mate value did not predict fulfillment of short-term preferences when controlling for long-term mate preference fulfillment, b = −0.05, p = .61. Participant’s long-term mate value also did not predict ideal partner short-term mate value, b = −0.05, p = .58, or chosen partner short-term mate value, b = −0.05, p = .29, when controlling for short-term mate values. Finally, participant’s short-term mate value did not predict long-term preference fulfillment, ideal partner mate value, or chosen partner mate value independent of participant’s long-term mate value, all ps > .10. Controlling for short-term mate value did not qualitatively change the relationship between long-term mate value and any of the three outcome variables, all ps < .001.

Discussion

Study 2 provided evidence that individuals high in Euclidean mate value do in fact experience greater power of choice on the mating market. Consistent with the Euclidean simulation from Study 1, participants strongly fulfilled their long-term mate preferences in Euclidean terms—achieving nearly 80% of maximum possible Euclidean preference fulfillment—and Euclidean long-term mate value predicted preference fulfillment, ideal standards, and partner mate value. These effects were further specific to long-term mate relationships: Participants did not fulfill their short-term preferences as strongly as their long-term preferences, and short-term mate value did not afford participants greater power of choice on the long-term mating market. However, because participants self-reported their traits and their partner’s traits, it is possible that participant biases, and not power of choice, account for the predictive power of Euclidean mate value. I therefore conducted Study 3 to assess the predictive power of Euclidean mate value when accounting for participant biases.

Study 3: Euclidean Mate Value and Power of Choice Accounting for Participant Biases

Study 3 had two aims: to replicate the results of Study 2 and to assess the ability of participant biases to account for these effects. Study 2 found that the pattern of effects diagnostic of Euclidean integration emerges in real human relationships, in that, people high in Euclidean mate value appear to experience greater power of choice. Yet, because participants reported on their preferences, themselves, and their partner, it is possible that the appearance of power of choice could be better explained by participant biases. Study 1 demonstrated that the power of choice correlations observed in Study 2 are unlikely to be explained by participants misperceiving their partners as better matching their preferences. Nonetheless, it is possible that participants who have inflated views of themselves might also set unrealistically high standards, overestimate their partner’s mate value, and overestimate the extent to which their partner matches their ideals. To test this possibility, participants in Study 3 completed the same measures as in Study 2 in addition to measures of self-deceptive enhancement and narcissism. If participant biases can explain the results of Study 2, these bias measures should account for Euclidean mate value’s predictive power.

Method

Participants

Participants were 264 people (134 female) in committed, long-term, heterosexual relationships recruited from Amazon’s Mechanical Turk. Participants were a subset of a larger sample of n = 342; 78 participants were excluded because they failed at least one of two attention check items. Participant recruitment was again targeted at a final n of 250 based on power analysis. Participants were M = 34.09 years old on average, SD = 10.22 years, and the median relationship length in this sample was Mdn = 48 months.

Measures

Participants used the same mate preferences scale from Study 2 to report their ideal long- and short-term preferences as well as rate themselves and their partners.

Participants, additionally, completed the self-deceptive enhancement component of the International Personality Item Pool version of the Balanced Inventory of Desirable Responding (Goldberg et al., 2006; α = .82). Participants responded to this inventory using a 7-point Likert-type scale to rate their agreement with statements such as “I always know why I do things.”

Finally, participants completed the narcissism subcomponent of the Short Dark Triad scale (Jones & Paulhus, 2014; α = .76), which asked participants to rate their agreement with statements such as “I insist on getting the respect I deserve” using a 7-point Likert-type scale. Participants completed these scales in randomized order. Because these scales tap overlapping constructs and because their scores were correlated, r(262) = .41, p < 001, I also constructed a composite participant rating bias score by conducting a principal components analysis on both scale items and extracting scores for only the first principal component.

Analyses

Analyses proceeded as in Study 2. To control for participant biases, I conducted an additional series of regression analyses predicting mate preference fulfillment, partner mate value, and ideal partner mate value from participant mate value while controlling for either participant self-deceptive enhancement or narcissism.

Results

Replicating Study 2

Study 3 replicated the results of Study 2. Participants again strongly fulfilled their long-term mate preferences (M = 0.79, 95% CI = [0.78, 0.80]), and did so more strongly than they fulfilled their short-term preferences (M = 0.73, 95% CI = [0.71, 0.74]), t(256) = 10.79, p < .001, d = 0.67. Figure 6 shows the zero-order relationship between participant long-term Euclidean mate value and the three outcome variables: long-term preference fulfillment, ideal partner long-term mate value, and chosen partner long-term mate value. As in Study 2, all effects were positive and significant: r(255) = .36, p < .001; r(256) = .48, p < .001; and r(256) = .53, p < .001, respectively. This pattern of results was again most similar to the Euclidean model relative to all other agent-based models from Study 1 according to all three similarity metrics (Figure 7).

Figure 6.

Power of choice relationships from Study 3.

Figure 7.

Similarity between the pattern of effects produced in Study 3 and the eight agent-based models from Study 1.

Participants’ long-term mate value again did not predict ideal partner short-term mate value, b = 0.05, p = .42, or chosen partner short-term mate value, b = −0.03, p = .41. However, in contrast to Study 2, but still consistent with hypotheses, participants’ long-term mate value emerged as a negative predictor of short-term preference fulfillment: b = −0.21, p = .01. Finally, participants’ short-term mate value again did not predict any of the long-term mating outcome variables, all ps > .24; controlling for short-term mate value did not qualitatively change the relationship between participant’s long-term mate value and any of the outcome variables, all ps < .003.

Controlling for participant biases

Participant rating biases did not account for the relationships between participant mate value and the three outcome variables. Participant’s long-term mate value remained a significant and positive predictor of long-term preference fulfillment, ideal partner mate value, and chosen partner mate value, when controlling for participant self-deceptive enhancement scores, participant narcissism, and their composite, all ps < .001. The participant rating bias variables in contrast had only scattered and relatively small effects on these variables. Self-deceptive enhancement predicted long-term preference fulfillment, b = 0.15, p = .03; however, narcissism and the participant response bias composite did not, both ps > .10. No rating bias variable significantly predicted partner mate value, all ps > .40. Self-deceptive enhancement negatively predicted participant ideal mate value, b = −0.09, p = .01. The same trend emerged for participant narcissism, b = −0.11, p < .001, and the participant response bias composite, b = −0.12, p < .001.

Discussion

Study 3 replicated and extended the results of Study 2. Participants high in long-term Euclidean mate value again showed evidence of experiencing greater power of choice on the mating market: People in general fulfilled their mate preferences strongly, again approaching 80% of maximum Euclidean preference fulfillment, but high mate value people better fulfilled their preferences, set higher mate value ideals, and tended to pair with higher mate value partners. Furthermore, these effects were specific to long-term mate value and long-term mating outcomes. Finally, and crucially, this result was not accounted for by participant biases: Neither self-deceptive enhancement, narcissism, nor their composite accounted for the predictive power of long-term Euclidean mate value. Overall, people high in Euclidean mate value appear to experience greater power of choice on the mating market because human mate choice psychology uses a Euclidean algorithm to integrate mate preferences.

General Discussion

Selecting mates based on multiple mate preferences requires a psychology capable of integrating preferences into summary evaluations of potential mates. Three studies provide insight into the computational design of this preference integration psychology. Across Studies 2 and 3, people strongly fulfilled their mate preferences in Euclidean terms, and people who were high in Euclidean mate value tended to better fulfill their mate preferences, set higher mate value ideals, and have higher mate value partners. Study 1 demonstrated that this pattern of results emerges in, and is relatively unique to, mating markets in which individuals use a Euclidean algorithm to integrate their preferences. Altogether, these findings suggest that human mate selection psychology integrates preferences according to a Euclidean algorithm.

This Euclidean algorithm appears to be a good model for human preference integration psychology, but it could also serve as a valuable tool for future mating research. Applying the Euclidean algorithm allows researchers to compute mate preference fulfillment, the mate values of people, their partners, and their ideals, as well as a variety of mate value discrepancy variables (e.g., Conroy-Beam et al., 2016). These constructs have been proposed to be related to a variety of outcomes beyond partner choice including choice of mating strategy (Landolt, Lalumière, & Quinsey, 1995), commission of infidelity (Buss & Shackelford, 1997b), and mate retention behavior (Buss & Shackelford, 1997a; Miner, Starratt, & Shackelford, 2009). With the Euclidean algorithm, mating researchers can test mating hypotheses using measures of preference fulfillment, mate value, and mate value discrepancies that directly reflect the design of the underlying psychology.

The Euclidean algorithm also need not be limited to mating research. Humans express preferences for a variety of social partners, including friends (Bleske-Rechek & Buss, 2001; Lewis et al., 2011), allies (Benenson, Markovits, Thompson, & Wrangham, 2009), and leaders (Blaker et al., 2013; Todorov, Mandisodza, Goren, & Hall, 2005). These social selection processes are likely handled by distinct psychological systems: Leader value would be of limited value in selecting a fitness-beneficial mate, and mate value likely does not discriminate optimally between potential coalitional allies. Nonetheless, these different psychological mechanisms face a similar computational task: integrating domain-specific preferences with information on potential partners into summary evaluations. Other social selection psychologies could, therefore, integrate preferences using Euclidean functions similar to that used by mate selection psychology. Researchers could apply the Euclidean algorithm in these social selection domains to compute constructs such as friend value, coalition value, or leadership value, which could provide insight into a variety of social selection and relationship processes.

Although the three studies presented here do provide evidence that the Euclidean algorithm is a good description of how human mate choice psychology integrates preferences, these studies do have important limitations that future studies could address. First, Studies 2 and 3 were based entirely on self-report. Studies that incorporate partner reports as well as the reports of third parties would provide critical data for further testing the Euclidean algorithm. Second, the studies here relied on reports on ongoing relationships. Stronger tests of the Euclidean algorithm would use preferences at one time point to predict future mate selections (Campbell, Chin, & Stanton, 2016). Furthermore, the Euclidean algorithm should be able to demonstrate power in predicting outcomes beyond those in ongoing relationships, including courtship behaviors and thoughts, emotions, and behaviors surrounding relationship dissolution.

The models used in Study 1 could be improved along several dimensions. Agents within the agent-based model do not have to engage in courtship but instead pair based on their relative and mutual attractions. Explicitly modeling courtship processes could provide insight into how people use information about their mate value and the mate value of others to decide whether and how to court their many alternatives. Agents also select mates in relatively small populations of mates that they could search exhaustively. However, in real life, humans live in shifting subgroups of larger city, state, national, and international populations. Each mating market we live in is just one of a larger metapopulation of markets: A person unsatisfied with the mates in any one market could move to another in hopes of better prospects. Yet, the global metapopulation of mating markets is far too large for any one person to search exhaustively and so individuals need decision rules to govern whether and how they search through this larger metapopulation. The Euclidean algorithm appears to be a good model of how people select among alternatives within mating markets, but other algorithms, such as aspiration algorithms (Miller & Todd, 1998; Todd et al., 2005), would likely perform better as models of how people search among alternative markets. Future research could model these market-level decisions alongside individual-level decisions to yield predictions about what combinations of algorithms people use to translate their ideal preferences into mating decisions.

In addition, all models in Study 1 assumed that mate preferences are integrated simultaneously, but preference integration could also be hierarchical. Some preferred traits are hypothesized to be cues of higher order constructs, such as fecundity, parenting ability, or investment ability. For instance, waist-to-hip ratio, body mass index, and shoulder-to-waist ratio appear to be used as indirect cues to underlying reproductive value, which itself then predicts body attractiveness (Andrews, Lukaszewski, Simmons, & Bleske-Rechek, 2017). It is possible that mate preference psychology uses other algorithms to integrate lower order traits into higher order constructs and applies Euclidean integration to integrate only at the top level of the integration hierarchy. Future research could test models that incorporate such hierarchical processes to test what algorithms best explain each level of preference integration.

The Euclidean algorithm itself does appear to perform well as a model of human mate preference integration, particularly compared with the alternatives tested here. However, the fit between the Euclidean model and the human data from Studies 2 and 3 was not perfect, suggesting this model can be further refined. There are, in fact, an infinite number of alternative models researchers could consider, in principle, and it is a near guarantee that some of these alternatives will perform as well or better than the Euclidean algorithm in explaining human data. For instance, the Euclidean distance is just one instance of a family of distance metrics, the Minkowski distances, an infinite number of which would be practically indistinguishable from the Euclidean distance. It would be computationally impossible to test all possible models of mate preference integration, but researchers can continue to compare plausible regions within the space of possible models. The relatively unique correspondence between the Euclidean model and the human data from Studies 2 and 3 suggests that the Euclidean algorithm is at least close to the algorithm actually applied by human mate choice psychology, but future research must continue to test alternatives against the Euclidean algorithm to find models that perform even better.

In this effort, researchers should also apply multiple methods for comparing alternative models. For example, although the pattern of effects found in Studies 2 and 3 did appear unique to Euclidean integration, the cosine and linear models in Study 1 did produce relatively similar patterns compared at least with the aspiration and curvilinear models. However, there are other reasons to believe these algorithms will be poorer models of human preference integration than their performance here would suggest. For instance, similar or identical models are outperformed by Euclidean integration in predicting attraction for both linear and cosine similarity integration (Conroy-Beam & Buss, 2017) and in competitive evolutionary simulations for linear integration (Conroy-Beam & Buss, 2016b). No one model comparison is likely to perfectly discriminate between all possible models of human preference integration, and so, future research should continue to test multiple models across multiple dimensions to determine what models perform best overall.

Despite these limitations, the results of these studies overall provide new evidence concerning the design of human mate preference integration psychology. The three studies reported here document novel relationships between Euclidean mate value and mating outcomes that are most consistent with the hypothesis that people high in Euclidean mate value experience greater power of choice on the mating market. This pattern of results suggests that a Euclidean algorithm is a good model for how human mating psychology integrates multiple mate preferences in mate choice and validates this algorithm as a tool for better understanding mate choice and social partner selection more broadly in the future.

Footnotes

Acknowledgements

I thank Mohammad Atari for helpful feedback on an early draft of this article.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Supplemental Material

Supplementary material is available online with this article.

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