[EM] Strongest pair with single transfer (method)

[Chris Benham]

Kevin,
Interesting. What (if any) harm would be done by applying this to the 
three candidates remaining
after the rest have been IRV-style eliminated?

Is there any actual criterion that this method meets but IRV doesn't?

Chris Benham



Kevin Venzke wrote:

>Hi,
>
>Here's an attempt at a method that behaves well in the three-candidate
>scenario with preferences based on distance on a one-dimensional spectrum.
>I would call it "strongest pair with single transfer" or "SPST". It
>satisfies LNHarm and Plurality, and doesn't suffer from the worst kind
>of burial incentive. It also satisfies Clone-Loser I believe, though not
>monotonicity.
>
>My idea was to come up with a method that, in the three-candidate case
>with distance-based preferences on a one-dimensional spectrum, could
>elect the inner candidate in the absence of a majority favorite. I also
>wanted to avoid truncation strategy (Approval, Condorcet), gross Plurality
>failures (as under MMPO), and the sort of burial strategy where you give
>a lower preference to a candidate whose supporters are not ranking your
>candidate.
>
>Definition:
>1. The voter may vote for one first preference and one second preference.
>2. The "strength" of a candidate, or pair of candidates, is defined as
>the number of voters giving such candidates the top position(s) on
>their ballots in some order. (This is as under DSC.)
>3. A pair of candidates has no strength, if it includes any candidate
>who is not among the top three on first preferences. (I don't like this
>rule, but it's needed for LNHarm.)
>4. If the strongest candidate is in the strongest pair, or stronger than
>the strongest pair, then this candidate wins.
>5. Eliminate the strongest candidate. The second preferences of his
>supporters may be transferred to the individual candidate strengths of
>the two members of the strongest pair of candidates.
>6. Now, the strongest candidate in the strongest pair is elected.
>
>examples:
>40 A>B
>25 B>C
>35 C>B
>
>Strongest pair is BC; strongest candidate is A. BC is stronger than A,
>so A is eliminated and 40 preferences are transferred to B's strength.
>B wins.
>
>35 A>B
>25 B>C
>40 C>B
>
>Here BC is again the strongest pair, but C is the strongest candidate and
>wins immediately unfortunately.
>
>This method is a lot like DSC, but never requires more than N^2 numbers
>to be counted, whereas DSC requires 2^N if you keep track of every set.
>The elimination doesn't create IRV's counting issues, since with only
>two preferences taken we can just count them all.
>
>The burial strategy works like this: Say it's A, B, and C, with B as the
>middle candidate. A is expected to be the strongest candidate. Then
>voters with the preference order B>A have incentive to instead vote
>B>C. This is because if BC is the strongest pair, A will be eliminated
>and hopefully transfer preferences to B. But if AB is the strongest
>pair, A wins outright. As a result of this strategy, it is possible that
>(despite the LNHarm guarantee) A voters would decline to give a second
>preference to B, so that B>A voters can't count on the A voters to
>give a second preference to B.
>
>It is only possible to eliminate the first preference winner, due to
>LNHarm. It's only safe to eliminate a candidate who was going to win.
>Otherwise it could happen that voters have incentive to weaken a pair
>involving their favorite candidate, in order to prevent an elimination
>that causes the favorite candidate to lose to the second preference.
>
>Limiting pairs to the top three FPP candidates is necessary for LNHarm
>when there are more than three candidates. Otherwise it could happen,
>say, that BC is stronger than BD is stronger than A, A is eliminated,
>and then C wins. Whereas if BC were weakened and BD were strongest, A's
>elimination might result in B winning.
>
>Monotonicity can be failed when the winner is not the FPP winner, he
>gets more preferences, changing which pair is strongest, and causing
>the other candidate in the pair to win.
>
>I ran some simulations to try to measure this method against others. When
>the only ballot types are A>B, B>A, B>C, and C>B, this method is identical
>to DSC. When all 9 ballot types are allowed, this method seems to be 
>strictly more Condorcet-efficient than DSC, although not by much.
>
>I found that IRV is more Condorcet-efficient than either, except in
>the scenario where only the four ballot types are permitted, and the
>proportions of the B>A and B>C ballots are divided by 5. There IRV is
>worse because it wants to eliminate B.
>
>(With the four ballot types, IRV can elect B as long as B doesn't have
>the fewest first preferences. That particular scenario is important to
>me, though. DSC can elect B unless, say, the A>B faction outnumbers the
>B>A B>C factions, and also the B>C C>B factions.)
>
>That's it for now.
>
>Kevin Venzke
>
>
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