[EM] Kemeny-Young Thoughts

[Kristofer Munsterhjelm]

On 16.02.2022 08:58, Forest Simmons wrote:
> Suppose you had a nice metric on a candidate space for measuring the
> disparity between members of the electorate, and you wanted to use the
> metric to find the most representative member of the electorate. How
> would you use that metric?
> 
> There are many possibilities, but let's consider three of them that are
> fairly natural and easy to understand:
> 
> Let V be the set of voters, and let K be the subset of V consisting of
> the candidates who managed to get their names on the ballot. 
> 
> 1. Elect the candidate k that minimizes the total distance to the  other
> voters, i.e. elect argmin{TotDist(k,V)|k in K} where TotDist(k,V) is the
> total distance from k to the other members of V.
> 
> 2. Elect the candidate k closest to the most representative voter,
> namely argmin{TotDist(v,V)|v in V}. This is analogous to the Condorcet
> dictum, "elect the candidate closest to the voter median."

These approaches make use of the ballots that the candidates cast,
right? That would seem to be more in the spirit of Asset than an
ordinary voting method. If there's a secret ballot, then the candidates
are incentivized to lie on their ballots; and if the candidates' ballots
are not secret, then the candidates have to predict the election
accurately while still making their ballots pull the outcome in their
direction.

There's nothing wrong as such with the second - it fits with the Asset
principle of offloading the strategic burden on the candidates
themselves - but one should be aware that it's not an ordinary voting
method and couldn't be used for choosing what movie to watch, budget
item to fund, or similar.

...

That makes me think, though. Could one say that the distinguishing
feature of proxy and Asset-type elections is that they violate
anonymity? This because the proxies are privileged in the sense that
their votes are amplified by however many other voters decide to back them.

Perhaps not so much for traditional Asset, where you first choose a
"parliament" that then negotiates until some winner crosses a threshold.
That method has multiple rounds: first voting for assets, then the
parliamentary formation, then the final winner is decided; and it
doesn't violate anonymity in either round.

But a one-shot Asset-like where you either designate a proxy (whose vote
you'll copy) or vote directly... would. I think.

-km