There's a lot of randomness involved in party leader selection, or at least with regard to candidate attractiveness. But we can say that, at the margin, a party that cares about winning and that relies more heavily on low-information voters ought to lean towards more attractive candidates at the margin.
I'd written a few years ago:
In equilibrium if we've a thick market of potential candidates, I can't see how this generates any particular inefficiency. Sure, it gives an additional dimension over which parties need to optimize in candidate selection, but in sufficiently thick markets, the tradeoff in moving from the slightly less attractive to the slightly more attractive candidate won't be that large. The only problem is if you've got thin markets such that the quality gap on other margins is large as you move up the beauty scale. But that too should be a disequilibrium phenomenon. They've said that politics is show business for ugly people. Well, if the returns to beauty start ramping up in political markets relative to other markets, more beautiful people start selecting into politics rather than other endeavours. Hamermesh found that the beautiful select into professions where beauty is rewarded; why should this be any different?Will Hayward at Auckland Uni put NZ candidate photos up for an audience of American raters, none of whom could be expected to know anything about the candidates' parties or positions.
The findings? Based only on photos, Laila Harré was seen as most competent, trustworthy, and attractive. Jamie Whyte was second from the bottom on attractiveness, with Hone stuck in last place.
We probably can't draw much from it. But it does seem to matter at the margin for low-information voters.
Note that, by photos, the competence ranking was Harré, Key, Peters, Whyte, Cunliffe, Flavell, Norman, Harawira, Turei, Craig, Turia. Expect that low information voters may well be assessing candidate competence on similar basis. At least some of these rank orderings seem out to me.