[EM] Juho reply, 21 Feb., 1053 GMT

[Juho]

On Feb 21, 2007, at 12:53 , Michael Ossipoff wrote:

> Juho replies:
>
> Do you mean that margins would be so "strategy inviting" that most  
> voters would turn to strategic voters (in practical real-life  
> elections) if margins are used?
>
> I reply:
>
> Yes, voters would be more likely to regret sincere ranking in  
> margins than in wv.

This and many other points referred to various differences between  
margins and winning votes and related criteria. My proposed way  
forward is at the end of this mail.

> WV is much more strategy-free. The difference is unidirectional.

I doubt the unidirectionality. I think the example I gave (Sincere  
votes: 49:A, 49:BC, 1:CB. Strategic votes: 49:A, 49:BC, 1:CA.) was an  
example of a situation where WV is vulnerable to a strategy and  
margins is not.

> But Minmax only scores the candidate according to his worst defeat.  
> That doesn’t tell what it would take to get rid of all of his  
> defeats and make him the CW.

I think minmax(margins) does give information on how many votes a  
candidates needs to become a Condorcet winner. I'll use an example to  
visualize what I meant.

A loses to B 40-50. A loses to C 30-45. A wins all the other  
candidates. If there would be 16 additional voters that would rank A  
first the 30-45 defeat would change to a 46-45 win and the 40-50  
defeat would change to a 56-50 win. 15 additional voters would be too  
little and 17th additional voter is not needed. One thus needs to add  
one to the worst margins defeat of a candidate to get the number of  
additional voters that the candidate needs to become a Condorcet winner.

> One of the advantages of wv over margins is that, in wv, offensive  
> order-reversal is easily thwarted by simply not ranking the  
> reversers’ candidate.

Does this mean that voters that are not sure what strategies other  
voters will use but who believe that strategies will be used should  
bullet vote their own favourite? :-) As I said, I'd prefer sincere  
ballots to strategic defences.

> Offensive order-reversal, the only thing that could cause a  
> strategy problem in wv (truncation causes a strategy problem in  
> margins), requires lots of co-ordination, many strategic voters and  
> has great risk of failure--especially in wv, where it’s so easily  
> thwarted, merely by not ranking the perpetrators’ candidate.
>
> In margins, a CW could be defeated by truncation even if it is  
> inadvertent, lazy, hurried, or otherwise non-strategic. But of  
> course the election could be stolen from the CW by strategically- 
> intended truncation too, in margins.

I think the best way forward would be to give practical examples of  
situations where the methods fail due to strategic voting. This would  
demonstrate that the theoretic vulnerabilities are also practical  
vulnerabilities. And this gives us the opportunity to estimate the  
probabilities too.

Maybe you can provide an example that demonstrates some really bad  
case where margins fail. I'll try to do the same for winning votes. I  
have no intention to prove that winning votes would be worse than  
margins in all scenarios. I'd like to see them roughly at the same  
level with respect to vulnerability to strategies. In addition to  
that I hope that the strategy related problems would stay at levels  
where they are not a probable threat in typical large scale public  
elections. Since US presidential elections are a well known study  
item on this list I propose to use that framework (nation wide  
Condorcet election).

Here's my example. It is in principle the same one I already used but  
now presented as a bit more realistic scenario. We have three  
candidates: D=Democrat, C=CentristRepublican, R=RightWingRepublican.  
I don't have any small party candidates, and that's maybe a deviation  
from realism, but let's do this simple scenario first.

Sincere votes:
21: D
21: DC
03: DR
03: CD
26: CR
26: RC

Many Democratic voters truncated since they were not interested in  
the Republican party internal battle between R and C.

The R supporters note that they could vote RD and get R elected (with  
winning votes). They spread the word among the R supporters and press  
too to reach the required number of voters. 6 out of the 26 R  
supporters follow the recommended strategy (=> 20: RC, 06: RD). R  
wins (with winning votes).

Is this scenario a credible real life scenario? Do you expect 6 out  
of the 26 R supporters to vote strategically? Opinions will be  
different in the poll that was used for planning the strategy and in  
the actual election. Does that make the strategy less credible? Is  
there a risk that this strategy would backfire? How often does it  
happen that supporters of one candidate have the possibility to  
influence the outcome of the election?

My target is to point out what the approximate probability level of  
minmax(winning votes) to fail as a result of strategic voting is. I  
don't consider counter strategies yet since I'm mostly interested in  
seeing how possible/probable successful strategic manipulation is in  
the first place.

Juho


P.S. One more example on winning votes and truncation. 49:AB, 48:BC,  
2:CA. A supporters truncate => C wins. Or alternatively sincere votes  
are 49:AB, 48:BC, 2:CB. In this case truncation by A supporters makes  
it possible for C supporters to vote strategically 2:CA => C wins  
(instead of B that was A supporters' second favourite).


		
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