[EM] Winning-votes intuitive?

[Adam Tarr]

 > Partial rankings are penalized.

I don't think it would be a strong exaggeration to characterize this as the 
crux of your argument.  You basically say, "Ranked Pairs ignores partial 
rankings, while SSD does not.  Since partial rankings are penalized, this 
allows those who are unaware of this in SSD to be victimized."

The addendum to this is that people are not really going to be more 
inclined to truncate than they are to order-reverse anyway.

 > I hope that no one
 > doubts that the word "penalized" is justified.  I
 > mean, if my favourite is A, then on average, any
 > complete ranking is better for electing A, than
 > ranking A alone.

I do doubt that the word "penalized" is justified.  My example shows 
multiple instances of the opposite being the case.

I guess the question of what constitutes "penalized" is an important 
one.  Are you saying that the voters are penalized relative to their 
sincere ranking, or penalized relative to a strategic order 
reversal?  Because there is a huge difference.  Moreover, the latter is 
irrelevant to the margins vs. winning votes debate.

Let's look at my example one more time:

Sincere ranking:

49:Bush>Gore
12:Gore>Bush
12:Gore>Nader
27:Nader>Gore

Now, who benefits and who is hurt by truncation?  Let's look at each faction.

The 49 Bush>Gore voters win the election for Bush by truncating in 
margins.  In winning votes, they fail to change the outcome.  In neither 
case does truncation hurt these voters.  The fact that order reversal helps 
these voters (assuming everyone else votes sincerely) is irrelevant to the 
discussion.  Remember, we're only seeking to find who is "penalized" by 
truncation.

The 27 Nader>Gore voters... yes.  They are penalized by truncation, no 
doubt.  This is equally true in margins and winning votes, however.

The second choice of the 12 Gore>Nader voters is largely irrelevant.  Nader 
is more or less guaranteed to lose big pairwise to Bush in this election 
anyway.  So truncation is neither good nor bad for them.

In the case of the 12 Gore>Bush voters, truncation is a poor strategy in 
margins.  It will have little impact unless there is a huge amount of 
order-reversal in the Bush camp, at which point it throws the election to 
Nader.  In winning votes, however, truncation more or less guarantees a 
Gore victory, regardless of order-reversal from the Bush>Gore voters.

So, if you're scoring at home, that's one clear penalty for truncation in 
either margins or winning votes, one totally irrelevant choice about 
truncation in either margins or winning votes, one case where truncation 
helps in margins but not in winning votes, and one case where truncation 
hurts a little in margins, but helps in winning votes.  It's worth noting 
that the one time truncation helps in winning votes, it enforces majority 
rule, while the one time it helps in margins, it allows a minority to 
defeat the sincere CW.

Let me repeat your previous statement:

 > if my favourite is A, then on average, any
 > complete  ranking is better for electing A,
 > than  ranking A alone."

I have seen no evidence to this effect.  What I have seen suggests that the 
effect of truncation varies wildly from case to case, and that election 
results in winning votes tend to be less negatively effected by truncation.

 > On the margins side, we don't want to impose any
 > particular penalty for leaving candidates unranked,
 > since we want this to be a reasonable option for
 > people.

Winning votes provides this option.  Margins doesn't really, since your 
ballot effectivelly gets randomly completed if you leave it incomplete.

 > This means we can't set up specific
 > penalties against insincere partial rankings without
 > mind-reading).  We note that although people can
 > gain through truncation, they can also lose by it.

True.  So our goal is to pick the system that seems to reward sincere 
rankings as oppose to insincere partial rankings.  From what I have seen, 
that would imply winning votes is a better method.

 > It's not like it's a good strategy in general.  We
 > note that if voters behave rationally the whole
 > issue is moot.

No strategy is good "in general".  Different situations demand different 
strategies.  But I'm not convinced that insincere partial rankings are 
always a suboptimal strategy in margins.  It seems reasonable that there 
could be a situation in margins where truncation will order the victories 
just so, while order reversal will push the winning margin high enough that 
another camp could manipulate the results even further with order-reversal 
of their own.

-Adam