[EM] Thoughts on Burial

[Jameson Quinn]

2010/7/17 Juho <juho4880 at yahoo.co.uk>

> On Jul 17, 2010, at 7:40 PM, Jameson Quinn wrote:
>
> To clarify my position:
>
> I think that, because of social dynamics which push voter groups towards
> symmetry (ie, B voters like A as much/little as A voters like B), honest
> condorcet cycles will be a fraction of what they would be in "impartial
> culture"-type models. Since such models usually give somewhere around 10%
> cycles, or a little more, I think honest cycles will be somewhere in the low
> single digits - 1%-4%. For this, I have little evidence, although it should
> be noted that Romania is not at all counter-evidence; one documented
> possibility in a large number of modern, polled elections is about what my
> proportion would have predicted. It is certainly not evidence against "most"
> cycles in a Condorcet system being due to truncation, as we have essentially
> 0 data on condorcet systems in public elections.
>
>
> Probability of honest cycles may vary between different societies and in
> time too. I also note that random vote models typically give more cycles
> than real world set-ups that may often have some fixed preference patterns,
> marginal parties etc.
>
> I commented earlier that near ties and non geographic preferences may
> create cycles. Also symmetric preferences and geographic (distance based)
> models may often have cycles.
>
> 3) Let's assume that there are three voter/opinion groups that form a
> triangle. Then we will nominate the candidates - one candidate from each
> group. It may well happen that the candidate that group A nominates is more
> on the B side of that group than on the C side of that group. And the same
> for the two other groups. As a result a natural cycle is quite well
> possible. Voters of each group will rank the candidate of their own group
> first. With good probability they will rank second that candidate of one of
> the other groups that happens to be close to one's own group.
>

Given the conditions you state, a cycle is at most 25% likely (say WLOG that
candidate A is on the "clockwise" side, then it's 50/50 for B and C to be
the same). Actually, the probability is a little less, because there will be
some voters who are farther from the mode of their bloc than the other two
candidates are, and if these groups are unequal, it could upset the cycle
balance.

I think the conditions will be close enough to your scenario at MOST half
the time. So that's down to 12%.

And I think that inter-voter dynamics will encourage the symmetrical groups
to grow. That is, if there are ABC and BCA voters, I think that some BCAs
will have friendly interactions with the ABCs, and come around to the BAC
position. This should cut some more off of the natural cycles.

>
>
> I think that the necessary conditions for truncation/burial to be a
> rational strategy will be much more common. It depends a lot on the average
> number of "serious" candidates per election, but assuming that with a
> Condorcet method that number would be somewhere between 2.5 and 5, with a
> minimum of 2... well, I don't want to pretend I've done the calculations,
> but my guess is that that would lead to somewhere between 20% to 60% of
> elections having a rational truncation which would affect the result. I'd
> imagine that a possible truncation would actually happen somewhere from 25%
> to 75% of the time. So honest cycles should be roughly 1%-4%, and truncated
> ones roughly 5%-45%. If these broad ranges are right, then truncated cycles
> will be 55%-98% of all cycles - probably 66%-90% - ie, "most".
>
> This is why I think that system performance relating to truncation strategy
> is at least as important as honest performance, at least for decent systems
> where the differences between honest performance are not too large.
>
>
> I first note that also strategic behaviour may vary greatly between
> different societies, partly because the political opinion space is
> different, but maybe more importantly because the morale and rules of
> behaviour of the society. In some societies people would enjoy use of all
> kind of more or less working strategic tricks while in others the whole idea
> of trying to cheat (e.g. crate an artificial loop) would be considered
> unacceptable (and any candidate that would recommend that would soon lose
> lots of support).
>
> In Condorcet rational strategic voting is not easy.
>

I used to thing this. But now I think that a simple approval-style
truncation (or, if truncation isn't allowed, burial) is possible. Say you're
an A>B>C voter. If you think that B is likely to win, and C is not likely to
win because there are far more people like you than honest B>C>A voters,
then you should (first-order rational strategy) just vote A (or,
equivalently, flip a coin between ABC and ACB). I understand that, given
second-order (defensive) strategy from B, this could elect C, and so is
perhaps in the final analysis not a good idea. It is certainly not as bad as
the situation in Approval, where this is simply a game of chicken between
the A and B voters.


> It is possible that after the election one can see that some well
> coordinated group of voters could have changed the result (assuming that
> other voters would all have voted sincerely). But this is still quite far
> from having a rational strategy available to the voters at the election day.
> I have asked people to write down rules that could be used in any Condorcet
> elections or in some particular Condorcet election. But I have not seen any
> such descriptions yet. Are there some clear rules that would make strategic
> voting rational in some elections? In typical elections (large, public, with
> independent voters and changing opinions) there are many problems like
> inability to coordinate the behaviour of the intended strategic voters,
> unwillingness of some to participate in the strategy, other possible
> strategies, changing opinions and variation in polls, optimistic people that
> believe in some nice outcome, too difficult strategic guidance that people
> will not follow, risk of backfiring strategies, voters voting against  / not
> supporting groups that try to "cheat" etc.
>

I acknowledge all of these issues. Still, I believe that between the small
probability of an honest cycle, and the small probability of a strategic
one, the latter is greater.

JQ
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20100721/62feeab5/attachment-0004.htm>