[EM] Kemeny-Young Thoughts

[Forest Simmons]

El mié., 16 de feb. de 2022 4:33 a. m., Kristofer Munsterhjelm <
km_elmet at t-online.de> escribió:

> 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's a possibility, but not what I had in mind. For example, in method
two, once you have found the secret anonymous ballot B that minimizes the
total distance to the other ballots, just assume that ballot B's favorite
is the candidate closest to ballot B. This ballot B could well be the
ballot of one of the candidates, but there is no way of knowing that. This
is the same reasoning that Kemeny-Young uses to identify the candidate
closest to its idealized ballot.

Another possibility is (for each candidate k) find the ballot B(k) that
minimizes the total distance to the ballots that rank k as favorite. Then
consider B(k) to be the position of candidate k in ballot space. That might
be the best approach for multi-winner K-Y.

Arguably either one of these inferences of the location of the winning
candidate is just as good as the (computationally expensive) idealized
ballot inference of Kemeny-Young.

That would seem to be more in the spirit of Asset than anh
> 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
>
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