[EM] Thoughts on Burial

Sat Jul 17 11:31:35 PDT 2010

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.

>
> 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. 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.

So, my claim is that in typical elections most often sincere voting is  
the best strategy. In countries where people are used to vote as told  
by their own party strategists (e.g. Australia) the probability of  
rational strategic voting is somewhat bigger. But in both cases I'd  
like to see first scenarios and _rational_ guidance to the voters that  
would work also in real life, not just on paper. I.e. guidance like  
"if opinion polls show that ... then vote so that ..." or "since  
opinion polls show that ... you should vote so that ...". Are there  
such cases? Are they common? Is it rational to say to the voters of  
Condorcet elections "just vote sincerely, that's the best strategy"?

Juho

>
> JQ
> 2010/7/14 Warren Smith <warren.wds at gmail.com>
> > I believe that Jameson Quinn is right when he says that most  
> Condorcet cycles are probably artificial,
> i.e. they are caused by strategic truncation or strategic burial.
>
> --For a real life example of a Condorcet cycle in a large national  
> election, see
>   http://rangevoting.org/Romania2009.html
> Contrary to Simmons' conjecture/intuition, this cycle seems to have
> been not "strategic," it was "honest" -- because the evidence for the
> cycle consists of pairwise-poll data, and there is no motivation for
> dishonesty in 2-man pairwise polls.
>
> Further, other real-world cycle examples (?) are noted, discussed 2nd
> half of section 4.
>
> --
> Warren D. Smith
> http://RangeVoting.org  <-- add your endorsement (by clicking
> "endorse" as 1st step)
> and
> math.temple.edu/~wds/homepage/works.html
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