[EM] Least Additional Votes. The importance of strategy.

[Juho Laatu]

Hello Mike,

Thanks for the comments. I agree with most of the stuff. Few comments 
follow.

Best Regards,
Juho


> You continued:
>
> This is based on the assumption that strategical voting is not that 
> easy in real life, at least not in elections where the number of 
> voters is large.
>
> I reply:
>
> It happens in every election in the U.S. People say that they're 
> abandoning their favorite to vote strategically. Millions do so.

I should have said "... strategical voting in _Condorcet_ methods ...". 
I thus mean that all Codorcet methods are pretty good in eliminating 
strategic voting. And the remaining cases (I think all of them are 
related to cycles) are not necessarily easy to use. I'm sort of hoping 
that in most cases in Condorcet elections it would be wiser to vote 
sincerely rather than try to do something strategical. Many of the 
voting methods in use today have one order of magnitude more problems 
than any of the Condorcet based methods does.

> The fact that the voters don't have good information on which to base 
> strategy has never stopped them from attempting to vote strategically, 
> by using the unreliable strategic information that they've heard from 
> their tv.

This is interesting. I believe that when Condorcet based methods are 
taken into use there really will be large number of people who will put 
the strongest competitor of their favourite candidate last on their 
ballot - just to make sure that she will not be elected. Government 
should thus be active and tell people that the voting method is good 
enough so that everyone can vote sincerely without the risk of helping 
the worst competitors when doing so. Unfortunately the remaining 
strategical voting issues in Condorcet methods leave space for all kind 
of stories and speculations about possible strategies. I hope the 
voters will not read this mailing list since they sure would get 
paranoid after only few mails :-).

> But the defensive strategy criteria are very much based on real life 
> need. That need, indicated by numerous conversaions with demoralized 
> voters, led me to propose the criteria.

I support all efforts to reduce the strategic voting related problems. 
I do however believe that there is also an upper limit after which new 
additional techniques bring more harm than benefits.

Let's make some definitions
VM1 = Best voting method if all the votes are sincere
VM2 = Best voting method
VM3 = Voting method that is best in eliminating strategical voting 
possibilities

What I'm desperately trying to prove is that in the family of Condorcet 
based methods VM1 is closer to VM2 than the discussions at this mailing 
list indicate (maybe even the same). I do support theoretical studies 
on this topic, but to me the question what is the best practical method 
for certain purpose is different from the question what method 
theoretically best in some respect (e.g. in eliminating strategies) 
(not necessarily a practical need).

I think strategy elimination is important. Condorcet does already most 
of it. VM2 may add some useful defence mechanisms on top of that. VM3 
is too much. I'm a bit cautious with some of the most complex and least 
practical strategy elimination proposals.

Possible problems of VM3 are unnecessary complexity and possibility of 
electing too often some other candidate than what VM1 (with sincere 
votes) would elect.

It is possible that VM3 is planned so well that when one sums up the 
impact of given strategical votes and VM3 behaviour, its results are 
practically equal to
what VM1 produces. In this case VM3 = VM2.

VM3 and VM2 may include recommendations to voters not to vote sincerely 
but to always use certain strategy when voting. Not a very nice 
property of a voting method but can be used if nothing better is 
available.

Another related deviation from the sincere voting of VM1 is that VM3 
and VM2 may try to guess what voters mean. I mean that if with votes V 
method VM2 produces result R2, then VM1 (that is different from VM2) 
may produce result R1 that is different from R2. Maybe VM2 has 
corrected a strategy that voters applied when voting V. But maybe 
voters were sincere. In this case VM1 would have produced the best 
result and the result should be R1, not R2.

> Must quit now. Will ask about Least Additional votes later. But it 
> sounds like Dodgson, which doesn't do well by criteria, including, but 
> not limited to, the defensive strategy criteria.

Close to that. It is actually MinMax with margins. People are too 
familiar with MinMax, so I wanted to give them few moments of fresh 
thinking before going back to their already well established opinions 
of MinMax. I think this new definition of MinMax may be better than the 
traditional one since it links the method to some concrete real life 
phenomena/needs ("additional votes", "mutiny elimination") and is easy 
to understand to normal people.