[EM] utilities, Gini, and lotteries

[Forest W Simmons]

Thanks to Jobst for clarifying the conditions under which various kinds 
of individual and social utilities can be justified.

A most important idea is that for social utility the average of two 
lotteries could have more utility than either lottery separately 
because of the social value of having utility spread out instead of 
concentrated.

This insight is especially important for Western democracies in which 
great pains have been taken to caulk up all of the trickle down leaks.

As Jobst noted, this fact makes the usual plain average rating method 
of range voting somewhat inappropriate for our democracies.  He has in 
fact justified the use of the Gini score which is a much more 
appropriate kind of weighted average.

In the deterministic case this just means that we should use range 
ballots and elect the candidate with the highest Gini score.

Of course, strategic voters would still vote at the range extremes, as 
in approval strategy, though the pressure to do so would be less.

To make the lottery version computationally tractable, one would have 
to limit the number of lotteries to certain standard combinations of 
the candidates as well as any lotteries that are specifically nominated 
before some cutoff date.

Indirectly through their range ballots the voters' individual utilities 
for the various lotteries are inferred.  Then the Gini scores for those 
lotteries yield their respective social utilities.

Jobst and I happen to like lotteries as instruments of fairness and as 
devices for foiling manipulation.  But it should be pointed out, that 
although his essay gives lotteries a central role, in that context it 
is primarily a theoretical tool for showing the existence of meaningful 
individual and social utilities in the presence of certain hypotheses 
concerning binary preferences between lotteries.

I hope that these rremarks are helpful.

Forest