[Election-Methods] USING Condorcet

[Juho]

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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