[Election-Methods] [EM] RE : Re: Corrected "strategy in Condorcet" section

[Juho]

On Jul 23, 2007, at 17:20 , Kevin Venzke wrote:

> Juho,
>
> --- Juho <juho4880 at yahoo.co.uk> a écrit :
>> Margins vs. winning votes is another long term discussion topic on
>> this list. There have been many opinions and the final conclusions
>> may be more difficult to draw than in the Range strategy question.
>
> I agree here.
>
>> 1) It can be debated if Condorcet methods are in practice (large
>> scale public elections) vulnerable to strategies. If not, then both
>> margins and winning votes are safe enough and other criteria can be
>> used to pick one of them for use.
>
> It's possible that a coordinated strategy may not be feasible, but  
> that
> is not the heart of the problem in my view.
>
> Referring again to this scenario:
> 49 A
> 24 B
> 27 C>B
>
> Under margins the C voters have great favorite betrayal incentive  
> without
> any other faction having to use a coordinated strategy.

Sorry about some delay in answering.

There certainly are many viewpoints to this scenario. I'll present  
one. Please point out if I missed some essential things that you  
thought I should answer.

In this example a single C supporter can indeed change the winner (in  
the case of margins) to B by voting B>C instead of C>B. The strategy  
is very safe since C supporters can assume that C will not win the  
race in any case.

The pattern that leads to this strategic option is a loop where
- A wins C clearly
- C wins B with a small margin (and low number of winning votes)
- B wins A with an even smaller margin (but high number of winning  
votes)

How about the weak spots then:
- The outcome is not that bad since there is anyway a majority that  
would elect B instead of A, and C was beaten too badly to even try to  
win (winning votes actually elect B without requiring strategic votes)
- This scenario assumes a natural loop (not very common, and this  
type of loop maybe even less common than loops in general)
- It is difficult to find a real world model that would lead to this  
kind of votes (what is the reason why voters voted as they did? do  
you have a story that would explain this election?)
- Some of the strategic votes could be natural in the sense that if  
the numbers above are the outcome of an opinion poll few days before  
the election, then some C supporters might give up voting C as their  
first option since C seems to be "a sure loser"

But of course the fact remains that in this scenario margins are more  
vulnerable to and encourage strategic voting. The weakest spot of  
this scenario is that it seems that it is not very likely to occur in  
real life. Maybe there are some variants with more credible "real  
life" numbers.

This problem is margins specific but so far I couldn't find the  
reasons why this would make margins generally fail (worse and with  
higher probability than winning votes) in real life (large scale  
public) elections. I gave some links to the winning votes problems  
cases. They (for example) seemed more probable in real life to me  
than this scenario. But I have not done a complete enough analysis to  
claim that margins would definitely beat winning votes and that the  
probability of this scenario would be low enough not to be a threat.

>> 2) There are as well cases where winning votes are more vulnerable to
>> strategies than margins. So the question is not one-sided.
>
> However, it is pretty clear that margins has a worse FBC problem than
> WV does. Simulations have shown this, but it can be argued  
> logically as
> well.

May be so. Is there some reason why FBC would be a key criterion in  
this case? I made some time ago some simulations on margins and  
winning votes on if some certain random voter group or any of the  
voter groups could (from their point of view) improve the outcome of  
the (sincere) election by voting strategically (in whatever way). The  
simulation gave margins somewhat better results than to winning  
votes. Maybe the results depend a bit on what one simulates.

> If margins outperforms WV in some respect, I'd like to be able to  
> state
> exactly how.

- to me the choices that margins make with sincere votes seem (not  
necessarily perfect for all needs but) clearly more sensible than the  
choices of winning votes
- some of the scenarios where winning votes have strategic problems  
appear to be more probable in real life than the problem scenarios of  
margins (this feeling is however based on only a limited number of  
cases and not a thorough analysis)
- margins are easy to explain and understand and justify to the  
voters/citizens => "least number of additional votes needed to win  
all the other candidates" (no need to talk about breaking loops and  
about complex algorithms)

Sorry about not providing any more exact answers. The first  
explanation above is very obvious to me. The second case is just an  
estimate. The third one is again a fact although "social and  
psychological" by nature.

I've often seen some formal properties of voting methods presented as  
final proofs of the superiority/inferiority of some particular  
method. I don't measure the benefits as number of proven theorems.  
Especially in Condorcet methods the problem cases are typically  
related to scenarios that are not very common in real life. Therefore  
I'd like to see the claims linked to real world examples that  
demonstrate the theoretical scenarios in real life situations and  
estimate their probability, harmfulness, ease of applying them, risk  
of backfiring strategies etc.

Juho

> Kevin Venzke
>
>
>        
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