[EM] Thoughts on Burial

[Jameson Quinn]

2010/7/23 Kristofer Munsterhjelm <km-elmet at broadpark.no>

> Jameson Quinn wrote:
>
>  I've been thinking recently about systems which enforce chiral symmetry,
>> making condorcet ties impossible. While it is possible to "solve" the
>> truncation/burial problem (eg, between two near-clones who split a weak
>> majority) in this way, I have not been able to come up with an acceptably
>> simple system. The closest I know of is "tournament seeding"-style,
>> condorcet-compliant (though not necessarily condorcet-based) systems, where
>> only certain pairwise races are considered. In such systems,
>> burial/truncation is a nonstrategy, period.
>>
>
> I think I read somewhere that elimination tournament methods must fail
> monotonicity. I do know that runoff-type elimination based on weighted
> positional methods (e.g. IRV being based on Plurality, and Borda-elimination
> being based on Borda) must fail monotonicity.
>

That seems wrong to me. A simple random seeding and binary-tree (as in world
cup elimination) pairwise tournament method is, as far as I can see,
monotone. However, if you base the seeding on random ballot, then it
probably does fail monotone.

If parties are a factor, you could seed based on last-election performance.
For instance, make a matrix of average-number-of-candidates-in-between, with
tied candidates counting as half, and seed one round at a time so that the
closest candidates face each other. New parties would be seeded randomly.
This method would be very easy to explain to any sports fan (even though my
seeding, unlike world cup seeding, would pair off near-clones - even two
strong near-clones - in the first round, so that mutual burial between those
two groups becomes counterproductive in later rounds).

The problem is, while this method avoids the near-clone burial problem (when
the seeding works), it is vulnerable to a more-general turkey-raising burial
strategy, which could lead to DH3-type pathology. Oh well.

JQ
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