On Jul 22, 2010, at 1:42 AM, Jameson Quinn wrote:
2010/7/17 Juho <[email protected]>
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.
Yes, in this type of societies the probability of a cycle is probably
below 12%, and there will be many kind of interactions. Societies are
more complex than the simplified models, so we may need to wait for
the real elections and polls to see how often there will be cycles in
real life.
Also near ties, non geographic preferences (e.g. only one topic of
interest per voter), linear opinion space, multiple dimensions, voter
distribution (tight groups vs. even distribution), mobility of the
voters, style of campaign (aggressive vs. co-operative, quickly
adjusted vs. fixed opinions), number of candidates (per grouping),
flexible nomination of new candidates on "good spots" etc. will impact
the probabilities.
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.
I agree that there may well be societies where strategic cycles are
more common than sincere cycles.
(Btw, sometimes it may be difficult so say if the cycle is strategic
or sincere if there are both kind of votes, and also because after the
election it is typically not possible to say which votes were
strategic.)
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)? If
voters make independent decisions we may get closer to a "noise based
model". Either random additional noise on top of sincere opinions or
noise that reduces the differences between candidates (maybe leading
to a near tie between many candidates). In many societies open
strategy recommendations may not be accepted, but private decisions
can not be controlled (nor observed very well). Answers on these
questions may be quite society dependent.
Do you assume that the strategies are rational or irrational? Will the
strategy be successful as planned? Or is there a reasonable chance
that the strategy will work, and is it probable that the strategy will
improve the result rather than make it worse?
Strategies may also be used by voters who fear that the worst
(credible) alternative will win, and therefore they may try any tricks.
Also strategies to make the position of the expected winner to look
weaker, or strategies that try to influence the outcome of the next
election already now are possible. In the latter case the strategy may
also be sincerity.
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".
(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.)
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.)
JQ
----
Election-Methods mailing list - see http://electorama.com/em for list info
