[EM] Winning-votes intuitive?

[Adam Tarr]

Despite the fact that this debate has been on the list since long before I 
showed up, I really think we're making progress.

I wrote and Blake responded

>>A beats B, 70% winning votes (25% losing)
>>B beats C, 52% winning votes (45% losing)
>>C beats A, 50% winning votes (40% losing)
>>
>>By virtue of a slight perturbation (the sort that would fall within 
>>polling error margins in the real-world, nonzero-information case) 
>>candidate A now wins the election.  In this case, if I (any many others 
>>like me) randomly vote B over C, we change nothing, while if I (any many 
>>others like me) randomly vote C over B, we may turn B's victory over C 
>>into a defeat, and we turn C into a Condorcet winner.  This causes the 
>>defeat of A, our favorite.
>When I talk about randomly filling out a ballot, it is something each 
>person would do individually.  The whole group wouldn't decide to vote B 
>over C or C over B en masse.  Now I understand what you meant by saying 
>this would require co-ordination.

That's not what I meant when I said that (in an earlier message).  What I 
meant was that I doubt most voters will take to the idea of random ballot 
completion on their own, so a faction's leaders would have to encourage 
their voters to do so.  Even if folks decide independently to randomly 
complete, some voters may have some inclination to cast the vote for the 
candidate they prefer ever-so-slightly between those bottom two.  So 
co-ordination from the top (random voting schemes based on the last digit 
of your phone number, for example) would probably be called for to 
guarantee a faction doesn't lean their "random" ballot completion one way, 
and hurt its chances.

But this is not really what the above example is about.  The above example 
simply shows that random ballot completion CAN hurt you, if you pick the 
wrong side.  There's no denying that.  But your point is well taken: if a 
large group of like-minded voters commit to voting truly randomly on the 
bottom of their ballot, then there is only a tiny chance that they will end 
up hurting their cause (only if their randomness ends up accidentally 
favoring one candidate), and they can help their cause in certain 
situations.  So this is an advantage of margins over winning votes.  The 
first and only one that has been demonstrated to me.

I have several responses to this weakness.  First, allow me to borrow from 
your favorite counter argument from when I was criticizing margins methods 
earlier on this thread.  While this random ballot completion can help a 
faction, all they are really doing is strategic order-reversal on half the 
ballots, while the bottom listings on the other half of the ballots don't 
change anything.  Needless to say, this means that you can do the same 
thing with order-reversal (or order fabrication, as it were) as you can 
with random ballots. The only time the random-ballot completion is actually 
the optimal approach is in the zero-information case, which of course is 
pretty rare in public elections.  The strategic truncation issues that can 
cause problems in margins methods have the same property, but this still 
bears mentioning.

Secondly, this tactic only works when one faction is aware that random 
ballot completion is a good plan, while the other faction is not.  If 
everyone randomly completes, then you have exactly the same results you 
would have if margins methods had been used.  Presumably, when it matters, 
all faction leaders will so advise their voters.  So in the realistic 
zero-information case (if that's not an oxymoron) winning votes and margins 
will produce about the same results.

Third, this failure caused by winning votes random ballot completion has an 
analogy in margins voting with strategic truncation.  Take the case

9 ABC
8 BCA
7 CAB
3 ACB
3 BAC
3 BCA

B>C 7
A>B 5
C>A 3

If the BAC voters strategically truncate to B, then C>A jumps up to 6, and 
B wins the election in stead of A.  Granted, this is not the 
zero-information case, but it shows that margins can fail for the natural 
circular tie with strategic truncation.  In winning votes, the BAC voters 
would have to actually order-reverse to get what they wanted.

The proper response to this strategy is for the CAB voters to bury their 
favorite and vote ACB, which is a more radical tactic than just truncating 
was.  So unlike most random completion problems, the best strategic 
response is more radical than the truncation that forced the response.

I fully realize that this same effect could have been caused by order 
reversal in winning votes methods (although not by random second 
place).  But I'd argue that it's much harder to convince a faction to swap 
positions on their ballot than to convince them to bullet vote their favorite.

Finally, and most importantly in my mind, is the situations when the 
weaknesses of margins and winning votes methods present themselves.  The 
only time random ballot completion in winning votes can cause a problem, 
but strategic truncation in margins cannot, is when there is a cyclic tie. 
Strategic truncation, on the other hand, can actually cause a Condorcet 
winner to lose.  My original example from the beginning of the tread 
illustrates this exact point.  Since the cyclic tie is, in my opinion, a 
relatively unlikely event, an election method that minimizes strategy when 
a Condorcet winner exists is very desirable.  In winning votes, only order 
reversal can bring down a Condorcet winner, but other, less invasive 
options exist in margins methods.

It comes down to how you think the public will react to various strategic 
incentives.  If you truly feel that the public will have no qualms 
whatsoever about any manner of strategy, and indeed that they will figure 
out the optimal strategy without any help from their faction leaders, then 
there is no real difference between margins and winning votes.  Both will 
occasionally be perverted toward undesirable results by a faction 
practicing order-reversal.  But in my opinion, certain strategic tactics 
will be more palatable to the public, and will be easier to sell.  Bullet 
voting, or strategic truncation, seems like BY FAR the easiest one to 
sell.  You're not asking the voters to "lie", you're merely asking them to 
"not tell the whole truth".  I expect lots of people would see it this 
way.  It is for this reason that I consider margins methods' strategic 
pitfalls to be more dangerous than those of winning votes methods.

A summary:

***** The strategic options that winning votes methods allow (and margins 
methods do not) only come up when there are cyclic ties, generally apply 
equally to many factions, and tend to cancel out between factions and 
produce identical results to margins methods.  The strategic options that 
margins methods allow (and winning votes methods do not) can come up when 
there is a Condorcet winner, generally apply asymmetrically to certain 
factions, and often require defensive voting changes on the part of other 
factions to counteract, including favorite betrayal. ******

>>The moral of the story?  Losing votes do matter just as much as winning 
>>votes in winning votes methods.  They just don't matter until they become 
>>winning votes.  I've heard the argument here that this is too sudden and 
>>sharp a change, since we suddenly switch from considereing ONLY the votes 
>>on one side to considering ONLY the votes on the other.  This is sort of 
>>a silly argument, since every election method has some boderline where 
>>all of a sudden one vote causes a completely different result.  How you 
>>count the votes (winning votes vs. margins, for example) only decides 
>>where this border falls; it does not make this border any less stark.

>Obviously there is going to be a sudden change between who wins.  On the 
>other hand, such a change doesn't commit me to believing that a strong win 
>for A has become a strong win for B.  Since winning votes gives a vote of 
>50 to 49 precedence over one of 49 to 4, it seems like winning votes 
>thinks the former is in some way more decisive, or in other words, 
>strong.  So, we can easily argue that the method goes from strong one way 
>to strong the other with a change of a single vote.  That's quite 
>different than saying  merely that the winner might change because of one vote.

My opinion, which you are of course free to disagree with, is that this 
difference only matters insofar as it determines which candidate wins the 
election.

When we examine winning votes vs. margins, the differences are clear: 
winning votes encourages random ballot completion in low-information 
elections, while margins allows strategic truncation to accomplish 
reversals that require strategic order-reversal in winning votes.  As I 
explained above, I find the problems with margins to be more 
problematic.  The actual tabulation methods that lead to these differences 
are, in the final analysis, sort of irrelevant.

One final thought.  on 3/20 I posted a message about Approval Completed 
Condorcet.  The idea was to use a graded ballot (ABCDEF, for example).  If 
there was not a Condorcet winner, then the candidate with the most approval 
votes (A's, B's, and C's in the case of ABCDEF ballots) wins the 
election.  In my initial analysis, this method seemed at least as good as 
the other Condorcet methods we like to discuss.  Furthermore, it seems like 
it could be an easier method to pitch, since the cycle-breaker is VERY 
intuitive.  So I guess what I'm asking is... does ACC render this whole 
debate meaningless?  Just a thought.

-Adam