On Jul 8, 2008, at 2:41 , Kevin Venzke wrote:
Ok, any scenario with or without Condorcet winners will do.
All we
need to show is that there are scenarios that are plausible
in real
life (large public elections) and where use of burial
strategy is
likely and successful (does more good than harm).
Do you have some
specific set of votes in your mind that we could analyse?
The same one. Everyone can be expected to cast full rankings
because they
have been assured that it's safe. A>B>C and B>A>C (in no order) are
the
most numerous sincere preference orders. One of these types may
actually
make up a majority of the voters. C>A>B and C>B>A sincere rankings are
together much fewer. Sincere A>C>B and B>C>A rankings are fewer still.
What I suggest is that some quantity of each of the A>B>C and B>A>C
factions will believe they're (perhaps only slightly) better off using
burial strategy than not. It's impossible to tell what that
quantity would
be, as there are pressures from both directions. The expectation
that no
one will use burial strategy is itself a pressure to use it.
In the purest successful scenario (where everyone in a faction votes
together), which as you know looks roughly like:
45 A>C>B (strategic)
40 B>A>C
15 C>B>A (if they instead vote C>A>B, the strategy does nothing)
There is a sensible background story here in that the C voters
appear to
be closer to B than A, and to eat into B's first preference total.
If A
voters can guess that A will place first, they may be more likely to
expect to gain from burial strategy. What would prove them wrong is if
the B voters defensively use burial strategy themselves. Would/
should they?
Maybe they should just hope for C to use favorite betrayal if they
like
B.
Ok, this is a good concrete example scenario. The votes are of course
simplified. Surely there would be also considerable number of other
kind of opinions than these three. But let's see first where these
simplified votes could lead to.
Sincere opinions:
45 A>B>C
40 B>A>C
15 C>B>A
It seems that C is an extremist candidate (at the B side of the
political map since they prefer B over A). In line with this
explanation it is natural that A supporters prefer B over C. It is a
bit more strange that all B voters prefer A over C. Maybe C is so
radical that all others hate him/her. (The nature of the scenario
will however stay quite similar even if there were also some B>C>A
voters.)
The A party or A proponents have a plan to bury B under C. They would
need more than 40 strategic voters to make the strategy work. That is
89% of the A supporters. In some large elections like the
Presidential election of the USA that sounds like a close to
impossible thing to achieve. This depends of course a lot on the
independence (=vote as they decide themselves or seek for advice from
the party or other opinion leaders and strategists) and morale (=is
it considered ok to try to cheat the method) of the voters. It is
also possible that A will lose some support due to the plotting.
What if the A proponents manage to get the required 89% strategic
votes or more to support their strategic plan? Then the C supporters
can use a compromise counter strategy and rank B first. If more than
5 of the C supporters will use this strategy that will nullify the A
strategy even if they manage to get 100% of the A supporters to
follow the strategy. Less strategic C voters needed if less than 100%
of the A voters will follow the strategy.
If the method uses winning votes then the B supporters may also use
truncation as their counter strategy. 30 votes or more (out of the
40) needed. That would be a threat to elect C if A voters will apply
the strategy.
A promoters will not have complete control of the A voters. I'd
expect many "lazy A voters" to bullet vote. That would also weaken
the chances of the strategy to work.
With these numbers it looks to me that it would not be probable that
A party would recommend strategic voting, or that it would work if
they would recommend it. It may be better to use some more
traditional forms of campaigning and try to make some of the B
supporters favour A (instead of making them angry by recommending the
plot).
With some other numbers the probabilities could be different. My
point is that I have not yet seen such numbers that would clearly
make Condorcet vulnerable to strategic voting in typical large public
elections (with independent voter decision making).
Theoretical examples on paper give complete information of the
opinions and allow complete control of (uniform) voter behaviour, and
it is easy to assume that opinions will not change before the
election, and that other voters will not apply any strategies and
will not react to the strategies by changing their sincere opinion.
But in real life elections the environment is very different.
Candidates also typically (at least in many countries) tend to
present themselves as good and sincere candidates until the last
minute (i.e. not as ones that would resort to strategies in order to
win).
(One more reason why A voters should not use burial strategy is that
if C is stronger than expected then their strategy might also lead to
electing C instead of B. The opinions will still change before the
election (when compared to the available polls) but in this example C
is so weak that would require quite significant changes in the
sincere opinions. If A supporters try to bury B that may however turn
many sincere B>A>C voters to sincere B>C>A voters.)
Juho
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