[EM] Margins vs. Winning Votes

[Juho Laatu]

Hello James,

Thanks for the comments.

On Jul 27, 2005, at 14:07, James Green-Armytage wrote:

>
> Hi Juho,
>
> 	Glad that you're still thinking about this fascinating issue (voter
> strategy in Condorcet methods).
> 	You have constructed an example in which margins is less vulnerable 
> than
> WV. However, I suggest that it is just as easy (if not more so) to
> construct an example in which the reverse is true.

I think the correct way forward would be to write those examples down 
and then see what we have and estimate then relative vulnerability (of 
winning votes, margins and pair-wise methods in general) to strategies.

> In my opinion, the key
> difference is that when strategy does become a concern, WV allows for 
> more
> stable preventative counterstrategies than does margins.

I think the main battle should be fought already before the 
counterstrategies will be applied. I mean that normal voters would 
probably be unable to understand and apply counterstrategies and having 
to deal with them would give a bad impression of the voting method. I 
tend to think that if people would need to stop voting sincerely and 
start using strategies and counterstrategies, it could be better to 
forget that voting method and use some simpler method instead (IRV?, 
approval?, two round runoff?). I'm however living in the hope that 
pair-wise comparison methods would in most cases be strategy free 
enough so that voters could trust the method and vote sincerely 
(without being afraid that the few remaining strategic voters (there 
will be some in any case) could get their way through).

> Not that WV is
> necessarily always stable, but that its instabilities are less severe 
> than
> margins when they occur.
> 	The pairwise comparisons in your example are B>C>A. The B>C defeat 
> has a
> bigger margin than the C>A defeat, but a smaller WV count. A reverse
> example can be constructed by flipping these two relationships, i.e.
> making it so the defeat against the potential "strategizer" has a 
> bigger
> WV count but a smaller margin than the defeat from the strategizer.
> 	I'll use a similar scenario. The Democratic candidate is A, the more
> moderate Republican is B, and the less moderate Republican is C.
>
> 30 AB
> 18 AC
11 B
> 16 BC
> 25 CB

One difference between the examples is that in my example Democrats 
left Republicans unranked while in your example Democrats always rank 
Republicans and Republicans themselves don't express opinion on "C vs. 
A". The former looks more probable in real life. Or maybe there are 
cases where also the latter type of partial ranking is common(?). Do 
you have some "real life explanation" why people voted like they did?

>
> Pairwise comparisons
> B>A 52-48
> A>C 48-41
> C>B 53-47
>
> 	This example is not immediately vulnerable using a WV method, but it 
> is
> immediately vulnerable using a margins method, in that the A voters can
> win by burying B.
> 	In my opinion, this incursion is more severe than the one in your
> example, because that changed the winner to a fairly similar candidate 
> to
> the sincere winner, whereas in this example the new winner is evidently
> quite different.

In your example winner was changed from a Republican to a Democrat. 
That is quite severe (I had however above some doubts about if this set 
of votes is probable in real life elections). A is on the other hand 
the most popular candidate (48% of the votes), almost as strong as the 
two Republicans together. In my example the new winner (C) was disliked 
by both republicans and democrats. That's also severe.

I should also calculate how easy/difficult it is to apply the different 
strategies (number of votes needed, risks etc.) but that's too much for 
now and I leave that for further study.

> Also, it is somewhat reassuring that BA voters (assuming
> that some B voters are BA) can prevent incursion in my example using 
> WV by
> truncating, whereas they would have to order reverse in margins to get 
> the
> same effect.

This is something that I don't think will happen in real life, and 
something I don't want to happen in real life. I'd be very happy if 
real life elections could be held without requiring voters to apply 
complex counterstrategies.

> 	A bit more about risk-reward ratio in your WV example. Yes, there is 
> not
> much risk of the C voters' strategy leading directly to the election 
> of A,
> if it is clear that A is a Condorcet loser. However, if word of the C
> voters' strategy gets out to the B voters, and causes alienation 
> between
> the two factions which leads to mutual truncation, A does win. Assuming
> that B and C are fairly similar, this means that the risk-reward ratio 
> may
> actually be fairly high.

As already noted I don't like counterstrategies (in real life 
elections). I however think the anger of the B voters is justified. B 
voters however don't win anything if they manage to make A the winner 
(unless one considers revenge as one type of victory :-). The game 
appears quite tricky if both B and C voters apply strategies and 
counterstrategies and try t react each others' anticipated voting 
behaviour.

I'll give these examples some more thoughts also after these initial 
comments. Producing stable conclusions may take time though.

For me one interesting point in this discussion is the fact that 
different strategy examples exist. If they are reasonably similar in 
all directions, I have some interest in favouring margins since I find 
it to be a more natural measure than winning votes is. I don't however 
want to jump to conclusions. I just note that various strategic 
problems exist and I hope they are not too serious to make Condorcet 
methods unusable in general. Rather than recommending use of strategies 
and counterstrategies I hope that strategies are unusable enough to 
allow people to vote sincerely. Maybe lack of exact information on how 
people are going to vote and dislike of strategic voting and voters 
will do the job.

Thanks again for the counterexample. I hope we get a good collection of 
them and good analysis of the associated risks and probabilities.

BR, Juho


>
> my best,
> James Green-Armytage
> http://fc.antioch.edu/~james_green-armytage/voting.htm
>
>
>> 20	A
>> 15	ABC
>> 10	ACB
>> 35	BC
>> 20	CB
>>
>> - Democrats have nominated candidate A.
>> - Republicans have nominated two candidates. In addition to their
>> normal mainstream candidate B they have nominated also a right wing
>> candidate C.
>> - All voters have taken position on Democrats vs. Republicans.
>> - Some Democrat voters have not taken position on the Republican
>> internal battle between B and C.
>> - All Republican voters have taken position on B vs. C.
>> - Democrats prefer B over C.
>> - Republicans prefer B over C.
>> - B is the Condorcet winner.
>> - In raking based real life elections it seems to be quite common that
>> voters don't give full rankings. This example has only three 
>> candidates
>> and therefore full rankings could be quite common. But the election
>> could have also considerably more than three candidates, in which case
>> partial rankings probably would be quite common. It is probable that
>> ranking candidates of competing party is less common than ranking
>> candidates of ones own party (just like in this example).
>>
>> Now, what if some of  the the 20 C supporters (C>B voters) would note
>> the weak position of C before the election and decide to vote
>> strategically C>A>B.
>> - in the case of winning votes C wins the election with 6 to 20
>> strategic votes (out of the 20 C>B votes)
>>     => quite efficient and risk free (if one has reliable opinion poll
>> results available) (and if others don't use other strategies)
>> - in the case of margins A wins the election with 11 to 20 strategic
>> votes (out of the 20 C>B votes)
>>     => not very promising as a strategy
>>
>