[EM] Margins vs. Winning Votes

[James Green-Armytage]

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

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. 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.
	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.

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
>