Summable 3RD (non-partisan proportional) method

[Jameson Quinn]

I've written several posts here about my favorite methods for single-winner and for partisan proportional FPTP replacement. The missing third use case is for nonpartisan proportional use — things like a city council.

For that, I support 3RD voting — 3-rating delegated. I've just revised this system so that it will be summable at O(N^2), essentially by consolidating all ballots which top-rate a given candidate into an overall average. (Ballots which top-rate multiple candidates are effectively split into one equal fraction which top-rates each and middle-rates the others).

It is, in theory, possible to take strategic advantage of this, but I think it's not practical. For instance, say that X and Y had 0.75 quotas each of hard support, and there was a strategic bloc of 0.3 quotas of XY supporters. That should not be enough to get both X and Y elected, but if the XY suporters found a candidate Z with 0.4 quotas of Z>W support, with no other votes for Z and few for W, they could vote Z>XY. When Z was eliminated, around .15 quotas would flow to each of X and Y. When W was eliminated, another .2 quotas each would flow to X and Y, thus putting both of them over the top — 1.8 quotas was strategically turned into 2.2 quotas. 

But, as I said, this is not practical. It relies on the fact that Z and W are both eliminated before X and Y. In practice, pre-election polling would not be anywhere close to precise enough to allow planning a strategy like this.

I think that 3RD would be a good method for nonpartisan or weakly-partisan situations such as city council elections. It's proportional in purely partisan scenarios (partisan-Droop-proportional; that is, Droop-proportional in cases where each voter top-rates one of several non-overlapping "party lists" and bottom-rates all others); it has the capacity to give voters some voting power at the level of intraparty factions (that is, more than a single candidate, but less than a full party); it's simple enough for voters (substantially more so than STV); and it's summable.

[Ted Stern]

Corrected link for 3RD voting:  http://wiki.electorama.com/wiki/Proportional_3RD_(3-rating_delegated)_voting

I like this -- it's basically a simplified ER-Bucklin quota-based reweighted voting, with options that make it more convenient for voters.  Still has the free-riding problem, but I don't think that is going to be a huge issue in city council type applications.

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