The Role of Attractiveness in Mate Selection: Individual Variation

This post re­ports on a por­tion of my anal­y­sis of Fis­man and Iyen­gar’s speed dat­ing dataset which bears on the ques­tion of how peo­ple se­lect ro­man­tic part­ners.


Note:
I made very sub­stan­tial ed­its to the sec­ond to last sec­tion of this post hav­ing posted it, ad­dress­ing ques­tions of gen­er­al­iz­abil­ity. I’ve also cross-posted to my blog.

Summary

  • Par­ti­ci­pants rated one an­other on sev­eral di­men­sions. The ma­jor­ity of vari­a­tion in the rat­ings is cap­tured by the av­er­age of the differ­ent rat­ing types: some peo­ple were re­garded as good over­all, and oth­ers were re­garded as not good over­all.

  • The sec­ond most im­por­tant source of vari­a­tion in the rat­ings given to par­ti­ci­pants is that some were re­garded as more at­trac­tive and fun than they were in­tel­li­gent/​sincere, and for oth­ers, the situ­a­tion was re­versed.

  • Broadly, when peo­ple had to chose be­tween part­ners who were seen as at­trac­tive and fun and part­ners who were seen as in­tel­li­gent and sincere, they had a mod­er­ately strong prefer­ence for part­ners who were seen as at­trac­tive and fun.

  • In­di­vi­d­u­als varied sub­stan­tially in how they re­sponded to the trade­off, with some show­ing very strong prefer­ence for peo­ple who were seen as at­trac­tive and fun peo­ple, and oth­ers showed vir­tu­ally no such prefer­ence.

The speed dat­ing con­text may be un­usual in that peo­ple make a de­ci­sion on whether or not to see some­body again af­ter only 4 min­utes of in­ter­ac­tion. On the other hand, some peo­ple do meet their part­ners in con­texts such as bars and speed dat­ing events where de­ci­sions are made based on brief in­ter­ac­tions. To this ex­tent, the em­piri­cal phe­nom­ena in data from the study are rele­vant to un­der­stand­ing mate se­lec­tion in gen­eral.

The Pre­dic­tive Power of Attractiveness

In How Sub­jec­tive Is At­trac­tive­ness? I de­scribed how the group con­sen­sus on some­body’s at­trac­tive­ness ex­plained 60% of the var­i­ance in peo­ple’s per­cep­tions of at­trac­tive­ness. My origi­nal pur­pose in writ­ing it was as back­ground for a dis­cus­sion of how much at­trac­tive­ness in­fluenced peo­ple’s de­ci­sions as to whether or not to see their part­ners again.

I touched on this in Pre­dic­tors of Selec­tivity and De­sir­a­bil­ity at Speed Dat­ing Events. The group con­sen­sus on at­trac­tive­ness is highly pre­dic­tive of how of­ten peo­ple wanted to see some­body again. I re­mem­ber be­ing slightly shocked upon first view­ing the graphs be­low:

If we av­er­age over all par­ti­ci­pants, we find that par­ti­ci­pants of above av­er­age at­trac­tive­ness had twice as many suit­ors as par­ti­ci­pants of be­low av­er­age at­trac­tive­ness.

There are ques­tions of how the group con­sen­sus on at­trac­tive­ness should be in­ter­preted: for ex­am­ple, how much it’s de­ter­mined by phys­i­cal ap­pear­ance as op­posed to other char­ac­ter­is­tics. But up to that am­bi­guity, the ques­tion of whether the con­nec­tion be­tween at­trac­tive­ness and de­sir­a­bil­ity was causal is a se­man­tic one — the group con­sen­sus on at­trac­tive­ness picked up on some char­ac­ter­is­tic that re­sulted in cer­tain peo­ple hav­ing many more suit­ors than oth­ers. If we define at­trac­tive­ness to be what­ever that char­ac­ter­is­tic is, then the con­nec­tion is causal by defi­ni­tion.

De­spite the strong pre­dic­tive power of the group con­sen­sus on at­trac­tive­ness, there was sub­stan­tial vari­abil­ity in how much peo­ple’s de­ci­sions were in­fluenced by at­trac­tive­ness, whether mea­sured by group con­sen­sus or by their own as­sess­ment. While 98% of par­ti­ci­pants had per­cep­tions of at­trac­tive­ness that over­lapped with those of the oth­ers in the group, only 93% of par­ti­ci­pants made de­ci­sions that were cor­re­lated with the con­sen­sus of oth­ers on their part­ners’ at­trac­tive­ness.

In­di­vi­d­ual re­spon­sive­ness to attractiveness

To vi­su­al­ize the dis­tri­bu­tion of the de­gree to which peo­ple’s de­ci­sions were in­fluenced by their part­ners’ at­trac­tive­ness, for each in­di­vi­d­ual, we form the an­gle be­tween the vec­tors the par­ti­ci­pant’s de­ci­sions, and the av­er­age at­trac­tive­ness of his or her part­ners, and then plot these an­gles. The two vec­tors are in some ways qual­i­ta­tively differ­ent, so the an­gles don’t give a good sense for how much some­body’s de­ci­sions were in­fluenced by at­trac­tive­ness in ab­solute terms, but they’re helpful for think­ing about how in­fluenced peo­ple were rel­a­tive to oth­ers.

An an­gle of 0 de­grees rep­re­sents perfect cor­re­la­tion while an an­gle of 90 de­grees rep­re­sents the per­son’s de­ci­sions be­ing or­thog­o­nal to the group’s con­sen­sus on his or her part­ners’ at­trac­tive­ness. An­gles greater than 90 de­grees rep­re­sent nega­tive cor­re­la­tion. One can see that the an­gle was about 90 de­grees for a small but sig­nifi­cant frac­tion of par­ti­ci­pants, while for oth­ers the an­gle is very small, ap­proach­ing 0 de­grees.

The ac­tual prefer­ences of the par­ti­ci­pants surely vary less than the above graph sug­gests if it’s taken at face value: the differ­ence be­tween those at the ex­tremes and those in the mid­dle would shrink with

  • A larger sam­ple of dates per person

  • Bet­ter es­ti­mates of group con­sen­sus (based on rat­ings from a larger num­ber of raters).

Still, the graph ren­ders it plau­si­ble that the weight that peo­ple gave to at­trac­tive­ness varied a lot, even if the vari­a­tion was smaller than it is in the graph.

We could pro­ceed to make “best guess” es­ti­mates of what the true dis­tri­bu­tion is, but we can get greater in­sight into what’s go­ing on by first adopt­ing a shift in per­spec­tive.

Over­all de­sir­a­bil­ity and the tradeoffs

Par­ti­ci­pants rated each other on at­trac­tive­ness, fun, am­bi­tion, in­tel­li­gence and sincer­ity, as well as over­all like­abil­ity. Rat­ings on the differ­ent di­men­sions were all cor­re­lated, some­times strongly. (More here). This is par­tially ex­plained by per­cep­tions of some­body on one di­men­sion in­fluenc­ing per­cep­tions of the per­son on other di­men­sions (the Halo Effect). It could be par­tially ex­plained by ac­tual cor­re­la­tions be­tween the un­der­ly­ing traits be­ing mea­sured. I’ll ex­plore pos­si­ble ex­pla­na­tions in greater de­tail in the fu­ture. From the point of view of un­der­stand­ing how peo­ple’s prefer­ences vary, the main point is that though we have 6 rat­ing types, we have fewer than 6 in­de­pen­dent of pieces of in­for­ma­tion: rat­ings of in­tel­li­gence aren’t just rat­ings of in­tel­li­gence, rat­ings of am­bi­tion aren’t just rat­ings of am­bi­tion, etc.

We would like to throw out the re­dun­dant in­for­ma­tion so that we can fo­cus on the es­sen­tials. A method that fa­cil­i­tates this is prin­ci­pal com­po­nent anal­y­sis (PCA), an au­to­mated pro­ce­dure that takes the 6 rat­ings as in­puts and re­turns an out­put of 6 weighted av­er­ages of the rat­ings (called “prin­ci­pal com­po­nents”) that are in­de­pen­dent of one an­other. The key point is that it’s of­ten the case that the pro­ce­dure com­presses much of the in­for­ma­tion pre­sent in all of the vari­ables into the first few prin­ci­pal com­po­nents (some­thing that the pro­ce­dure de­signed to do), and that we can dis­card the other prin­ci­pal com­po­nents with lit­tle cost, re­duc­ing the num­ber of vari­ables that we need to con­sider.

If we ap­ply PCA to the 6 rat­ings, the first com­bi­na­tion that the pro­ce­dure gives is a weighted av­er­age where each rat­ing gets al­most equal weight:

good= 4* (At­trac­tive­ness) + 5*(Like) + 4*(Fun) + 4*(In­tel­li­gence) + 4*(Am­bi­tion) + 3*(Sincer­ity)

This can be thought of as cor­re­spond­ing to over­all fa­vor­able im­pres­sions of some­body, so I named it “good.” It cap­tures roughly 60% of the in­for­ma­tion that was in the origi­nal rat­ings.

The sec­ond weighted av­er­age that PCA gives is not nearly as sym­met­ric:

trade­off = 4.5*(At­trac­tive­ness) + 3*(Like) + 3*(Fun) — 6*(In­tel­li­gence) — 2*(Am­bi­tion) — 5*(Sincer­ity)

This prin­ci­pal com­po­nent picks up on the fact that af­ter the vari­a­tion picked up on by the first prin­ci­pal com­po­nent, the sec­ond largest source of vari­a­tion comes from those who were rated fal­ling on a spec­trum be­tween the two poles

at­trac­tive, fun and lik­able <-------------> sincere, in­tel­li­gent and ambitious

The first cluster of traits is more closely con­nected with main­stream ro­mance than the sec­ond cluster of traits, which are thought of as pos­i­tive, but less rele­vant.

The”trade­off” com­bi­na­tion cap­tures roughly 20% of the in­for­ma­tion in the origi­nal rat­ings. So to­gether, the first two prin­ci­pal com­po­nents cap­ture 80% of the in­for­ma­tion in the origi­nal rat­ings. We could look at the rest of the com­bi­na­tions that PCA gives us, but do­ing so would com­pli­cate the anal­y­sis with­out tel­ling us much more.

In­di­vi­d­ual differ­ences in ro­man­tic preferences

Hav­ing ex­tracted the two prin­ci­pal com­po­nents “good” and “trade­off”, we can ex­am­ine how par­ti­ci­pants vary with re­spect to how their de­ci­sions de­pend on their part­ners’ lev­els of each. Par­ti­ci­pants didn’t vary very much with re­spect to their re­spon­sive­ness to the “good” di­men­sion. It’s more in­ter­est­ing to ex­am­ine how peo­ple differed with re­spect to prefer­ences on the “trade­off” di­men­sion.

As back­ground con­text, if we’re con­tent not to take into ac­count differ­ences in ro­man­tic prefer­ences, we can model the prob­a­bil­ity of a par­ti­ci­pant’s de­ci­sion be­ing yes by us­ing a lin­ear model for the log odds ra­tio:

LOR ~ 2*good + trade­off + (gen­eral will­ing­ness to see part­ners again)

The fact that we’re adding the trade­off term rather than sub­tract­ing it cor­re­sponds to peo­ple tend­ing to fa­vor at­trac­tive and fun part­ners over in­tel­li­gent and sincere part­ners, when forced to choose.

To in­di­vi­d­u­al­ize the model while at­tempt­ing to cor­rect for the vari­a­tion that one would ex­pect by chance, I fol­lowed An­drew Gel­man’s sug­ges­tion and used Bayesian hi­er­ar­chi­cal mod­el­ing. We re­place the equa­tion above with

LOR ~ 2*good + (per­sonal trade­off co­effi­cient)*trade­off + (gen­eral will­ing­ness to see part­ners again)

where “per­sonal trade­off co­effi­cient” is a con­stant that de­pends on the in­di­vi­d­ual mak­ing the de­ci­sion.

The plot be­low shows the dis­tri­bu­tion of best guess es­ti­mates for the per­sonal trade­off co­effi­cients. The ti­tle of the plot is a loose de­scrip­tion of the “trade­off” prin­ci­pal com­po­nent, the pre­cise defi­ni­tion of which I gave above.

The left­hand tail cor­re­sponds to some peo­ple hav­ing ex­hibited vir­tu­ally no prefer­ence for at­trac­tive and fun part­ners over in­tel­li­gent and sincere part­ners. The right­hand tail cor­re­sponds to some peo­ple’s prefer­ence be­ing al­most twice as strong as av­er­age.

What this means in tan­gible terms

In my first draft of this post, I post­poned dis­cus­sion of statis­ti­cal sig­nifi­cance un­til later, but I sub­se­quently re­al­ized that I could ad­dress it suc­cinctly.

I formed the graphs be­low by:

  • Es­ti­mat­ing par­ti­ci­pants’ co­effi­cients based on the first 65% of the dates that they went on. Th­ese dates are the train set for our model.

  • Form­ing a “high” and “low” groups of par­ti­ci­pants ac­cord­ing to whether their co­effi­cients were in the top or bot­tom 13rd.

  • Restrict­ing con­sid­er­a­tion to those dates that were not in the first 65% of dates. Th­ese dates are the test set for our model.

Thus, the dates that I used to es­ti­mate the co­effi­cients are com­pletely dis­joint from the dates that I used to form the graphs, so that we get un­bi­ased es­ti­mates for the ro­man­tic prefer­ences that the two groups of peo­ple would show in con­texts similar to those of the study.

The first graph shows the fre­quency with which peo­ple’s de­ci­sion was ‘yes’ as as a func­tion of their part­ners’ at­trac­tive­ness level.

The slope is slightly larger for the the group with high co­effi­cient: you can see that the ini­tial differ­ence be­tween the two groups in se­lec­tivity shrinks as one passes from part­ners with low at­trac­tive­ness to high at­trac­tive­ness.

The vi­sual ap­pear­ance of the graph un­der­states the differ­ence be­tween the two groups: the high group vir­tu­ally never ex­pressed in­ter­est peo­ple low­est part of the at­trac­tive­ness spec­trum, whereas peo­ple in the low group were sev­eral more times more likely to. This comes across more clearly if we re­place the per­centage on the y-axis with the cor­re­spond­ing Log Odds Ra­tio . Here “odds” has the same mean­ing that it does in gam­bling (e.g.Roulette) and “log” refers to “log­a­r­ithm.” In the graph be­low, the 0 on the y axis cor­re­sponds to de­ci­sions be­ing yes 50% of the time, and an in­crease of 1 along the y-axis cor­re­sponds to the odds of a yes de­ci­sion in­creas­ing by 2x:

From this, one sees that while the high group was ~4x more se­lec­tive than the low group when it came to part­ners at the low end of the at­trac­tive­ness, it was only ~ 1.5x as se­lec­tive as the low group when it came to part­ners at the high end of the at­trac­tive­ness spec­trum.

The cor­re­spond­ing graphs with at­trac­tive­ness re­placed by in­tel­li­gence and sincer­ity are

(Note the differ­ence in scales on the axes: there was much less vari­a­tion in per­cep­tions of sincer­ity and in­tel­li­gence than there was in per­cep­tions of at­trac­tive­ness.)

One sees that past a cer­tain point, the high group is not re­spon­sive to in­creas­ing sincer­ity and in­tel­li­gence, whereas the low group is.

Of course, the high group and the low group don’t differ most with re­spect to their re­spon­sive­ness to at­trac­tive­ness, or in­tel­li­gence, or sincer­ity as in­di­vi­d­ual traits. They differ the most in how they re­spond to a trade­off be­tween at­trac­tive­ness/​fun and in­tel­li­gence/​sincer­ity. The graph that de­picts this is:

In pass­ing from part­ners for whom the trade­off term is low­est to part­ners for whom its high­est, the odds of be­ing se­lected by mem­bers of the low group in­crease by 5.5x, whereas the odds of be­ing se­lected by the mem­bers of the high group in­crease by only 1.4x.

The differ­ences be­tween the groups cor­re­spond to gen­er­al­iz­able phe­nom­ena. In fact, I knew that the differ­ences are statis­ti­cally ro­bust and gen­er­al­iz­able be­fore even do­ing a train/​test split as I did above. What made it ob­vi­ous to me is that the trade­off co­effi­cient cor­re­lates with many other fea­tures of the par­ti­ci­pants that were col­lected prior to the events...

To Be Con­tinued...

The ques­tion now arises: who are the peo­ple who lie at the two ends of the con­tinuum be­tween rel­a­tive prefer­ence for at­trac­tive­ness/​ fun and rel­a­tive prefer­ence for in­tel­li­gence /​ sincer­ity? How did they spend their time? What ca­reer paths did they pur­sue? How did mem­bers of the op­po­site sex view them?

I’ll offer par­tial an­swers to this ques­tions in my next post. Read­ers who are in­trigued can take a look at the sur­vey in­stru­ment for a list of fea­tures pre­sent in the dataset, and guess which fea­tures cor­re­lated with the per­sonal trade­off co­effi­cient.