Best counting methods?


#22

We are just gearing up to kick this project off. This will be a select group, but anyone who is interested is welcome to send me an email or give me a call. sara@equal.vote 971-222-9364


#23

One way you could do it is with pairwise comparisons. Have the voters pick their honest favorites, and simultaneously give the candidates their own utilities i.e. they are voters too. This utility needs to be correlated somehow, perhaps randomly, to the utility distribution of the candidates’ voters. After the election, there would be X number of seats to be filled and X number of top asset-holding candidates. Every candidate not in the top X should compare all other candidates (other than themselves) to a member of the top X, and “offer” their votes if there is someone better. You could simulate this over a few “turns”, with votes being reallocated until there’s a Condorcet equilibrium or cycle. Repeated elections show how voters might change preferences as a result of previous elections i.e. they seek to either consolidate or split their votes based on the negotiation efficiency of their previous favorite within the turns. 7 turns, to represent a week of negotiations might do well.

Finally, you’d want some way to show how negotiation of policy can either improve or worsen utility, so perhaps factor in “candidate sympathy” or cross-utilities i.e. the candidate shifts on everyone else’s utility distributions as a result of conceded policies between negotiation turns. Each candidate would have a certain amount of sympathy, and voters might factor this in when factoring their preferences between elections. The barebones of this model is the pairwise, Condorcet-like step, though; everything else is dressing.


#24

Well, as for candidate utility correlating to voter utility, you can just use a 1D or 2D issue space, and have the candidates prefer each other as voters prefer candidates.


#25

Here is a worked through example (warning - long, boring, and some steps are skipped/slightly off):

3 winners, 7 candidates: Extremely Liberal (el), Very Liberal (vl), Liberal (l), Moderate, Conservative, Very Conservative, Extremely Conservative

Votes: el 20%, vl 16%, l 10%, m 10%, c 14%, vc 10%, ec 20%

We want the following winners: Very Liberal, Moderate, and Very Conservative

The current winners (cw), as measured by which 3 candidates have the most votes after a turn: el, vl, ec

To start off, let’s have multiple candidates offer votes at once. Each candidate’s first preference is themselves, followed by the extremist of “their side”, then the other side, etc. The Moderate starts by favoring themselves then the Conservative.

Decisions made by current losers: l prefers vl, m prefers c, c prefers vc, vc prefers ec

el 20%, vl 26%, l 0%, m 0%, c 10%, vc 14%, ec 30%

Current winners (cw) - el, vl, ec

m prefers vc, c prefers ec

el 20%, vl 26%, c 0%, vc 10%, ec 44%

cw - el, vl, ec

m prefers ec

el 20%, vl 26%, vc 0%, ec 54%

cw - el, vl, ec

Now that we’re left with only 3 candidates with votes, we can run sequential checks - is there any candidate who is “worst-off” i.e. they lack the most possible representation among the winners?

m prefers c>l>vc>vl

el 20%, vl 26%, c 10%, ec 44%

cw - el, vl, ec

c prefers c>vc>m>ec

el 20%, vl 26%, c 24%, ec 30%

cw - vl, c, ec

m prefers l>vc>vl

el 20%, vl 26%, l 10%, c 14%, ec 30%

cw - el, vl, ec

m prefers vc>vl

el 20%, vl 26%, c 14%, vc 10%, ec 30%

cw - el, vl, ec

c prefers vc>m>ec

el 20%, vl 26%, vc 24%, ec 30%

cw - vl, vc, ec

m prefers c>l>vc>vl

el 20%, vl 26%, c 10%, vc 14%, ec 30%

cw - el, vl, ec

m prefers l>vc>vl

el 20%, vl 26%, l 10%, vc 14%, ec 30%

cw - el, vl, ec

m prefers vc>vl

el 20%, vl 26%, vc 24%, ec 30%

cw - vl, vc, ec

el prefers l>m>c>vc

el 0%, vl 26%, l 20%, vc 24%, ec 30%

cw - vl, vc, ec

el prefers m>c>vc

el 0%, vl 26%, m 20%, vc 24%, ec 30%

el prefers c>vc

el 0%, vl 26%, c 20%, vc 24%, ec 30%

l prefers m>vl

vl 16%, m 10%, c 20%, vc 24%, ec 30%

cw - c, vc, ec

el prefers vl>l>m>c

vl 36%, m 10%, c 0%, vc 24%, ec 30%

cw - vl, vc, ec

m prefers m>all others

vl 36%, m 20%, vc 14%, ec 30%

cw - vl, m, ec

After skipping a few steps…

vc prefers vc>all others

vl 36%, m 20%, vc 24%, ec 20%

cw - vl, m, vc

This is our desired winner set! Are there any candidates who can safely change this?

el can’t shift votes without hurting vl, and vl is el’s highest viable preference

same for vl

l can’t shift votes without hurting m, and m and vl are l’s highest viable preferences

c can’t shift votes without hurting vc, and m and vc are c’s highest viable preferences

ec can’t shift votes and change the outcome, without helping to elect a lower preference over a higher preference!

Keep in mind, in some simulations the candidates may wish to split their votes i.e. vc gives 5% of their votes to c, and 15% of their votes to ec.