[EM] Thoughts on Burial

[Jameson Quinn]

>
> I agree that there may well be societies where strategic cycles are more
> common than sincere cycles.
>

It seems that the two of us have a fair degree of agreement, let's hear from
others what they think.


>
> There are some interesting questions on the nature of the cycle and
> strategies.
>
> Do you assume (in the scenario where strategic cycles are common) that the
> voters would be coordinated (by parties or by media) or if the voters would
> make the strategic decisions themselves (maybe based on general poll and
> theoretical strategy related information from media but not voting directly
> as recommended by some central entity)?
>

I believe that a truncation-type strategy is simple enough that it will
occur to voters on their own. Both before the vote, and in the context of
post-facto analysis of "why did my candidate lose", when people are very
prone to find relatively sophisticated rationalizations. In the latter
context, while it would obviously not affect the outcome of the given
election, it would be toxic to the system and encourage division and silly
strategy in later elections. A good system, one in which its defenders can
make the strongest possible statement that "no, that's impossible", is
therefore desirable.

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.

(BTW, I think that the media is pretty hopeless in terms of helping voters
understand strategy; if we can't agree on things on this list of
knowledgeable people, how can you expect a clear, unanimous message to
emerge from the soup of interest and stupidity that is the punditocracy?
Even if the good analysis is a plurality at 40% of the media, while 60% is
three-different-kinds-of-wrong, then a naive voter gets nothing much from
that.)


> Do you assume that the strategies are rational or irrational?
>

There will certainly be both kinds, but any rational ones will have a
long-term competitive advantage and come to be most common.

The Condorcet elections that have been held so far do have not had (as far
> as I know) any sincere nor strategic top level cycles (nor any known
> strategic voting in general), so the probabilities may be small. But things
> may well be different e.g. when Condorcet methods are introduced in more
> strategic societies. Australia is maybe the best example on how there may be
> also societies with party led strategic voting in ranked vote based
> elections. I'm however not aware of any top cycles there either. In the
> Australian style strategic voting where voters vote as told in (e.g.) in the
> how-to-vote cards one could have also rational strategies. I however note
> that I still have not identified a single generic rule (nor
> election/situation specific advice) that would make it practical for single
> independent voters or even well coordinated groups to apply a rational
> strategy in typical real life elections. I use term "rational" here as "is
> likely to improve the expected outcome/winner(s) of this election".
>

In Australia (IRV), the clear strategy is to vote in a plurality-like way.
That is, between two near clones A and B who share a majority, supporters of
A, the one with least support from C voters, should betray and vote BAC. In
the absence of such a strategy from A voters, C voters should dishonestly
vote CAB, under the assumption that BCA and ABC are more common than BAC and
ACB. Both of these strategies are simple enough to describe, especially if
there's a pseudo-one-dimensional issue space. The favorite-betrayal one, if
correctly applied, increases social utility and would probably dominate and
suppress the burial strategy (since it's an effective defense). But as we
can see with plurality, it also decreases incentives for conciliation from
candidate B towards the A voters, allowing party B to become more corrupt
over time.

The reason that you cannot see evidence of these strategies in Australian
"party ballots" is that they are rational from a voter's perspective, but
unhelpful from a party's.


>
> (One strategy that might come close to being rational is intentional
> looping of three candidates of the competing party in some Condorcet methods
> that allow this strategy to work. But in real life this is not a very common
> scenario. Having a competing party that is likely to win and has three
> candidates that are almost tied and can be looped if one agrees the looping
> direction and communicates strategic voting advice (including choice of
> three random ways to vote) to all potential strategists, avoiding others to
> break the cycle etc.)
>

I agree that this is rational but unlikely.


>
> Juho
>
>
> P.S. One note on how voter behaviour could be modelled. A simple (and I
> think reasonably credible) way to include also non geographic opinions in
> the voter model is to give each topic (dimension) a voter specific weight.
> It may be quite common among voters that they give more weight to one or few
> particular topics that is on top of their agenda (either in these elections
> or also in long term). This leads to weight profiles like 5-3-2-1-1-1-0-0-0.
> A purely geographic profile would be 1-1-1-1-1-1-1-1-1. (Another way to
> improve the simplest voter models would be not to use even or simple
> distribution function based voter distribution but to introduce also some
> irregularity here => maybe more on this later.)
>
>
I am interested in investigating a simple two-dimensional model, in which
voters are normally distributed around (say) (1,1), and the weight of each
dimension for a given voter is proportional to its value. Condorcet cycles
are possible in such a model. If you normalize the total amount of utility
of each voter, then the social optimum is still near (1,1) (depending a bit
on your distance metric), but there would be a natural tendency for
candidates to collapse to near the x=y diagonal. That is to say, in a
situation where there are several dimensions with a relatively-indifferent
majority and a single, more-extreme minority, the parties will collapse
towards extreme-versus-not, even if the dimensions are actually orthogonal
among voters. (The funny part is that probably both conservatives and
liberals in the US two-party system would say "That's true, and the other
party are the extremists". That is not to say that there aren't objective
measures of which side truly is more a coalition-of-orthogonal-extremes,
just that there would be debate.)

JQ
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