[EM] Winning-votes intuitive?

[Adam Tarr]

>Are you claiming that it is always, or generally, a bad idea to give a 
>complete ranking in RP.  I believe that to be false.  If you don't have 
>any particular strategic knowledge, you should give a full ranking.

I agree, it is unlikely that this is always the case.  In my example, 
however, I have shown that a full & honest ranking makes Gore the Condorcet 
winner.

>Certain strategic knowledge can make it rational to order-reverse. 
>Sometimes in these situations you can get away with truncation instead of 
>order-reversal, although this is more likely to fail.

Order-reversal is the more extreme tactic and is more likely to require 
explicit coordination to work.  The more robust the system is to weaker 
manipulation, the harder to manipulate the results.

In my example, with Ranked Pairs, the Bush voters get the desired results 
if at least 48 of 49 voters truncate, or if at least 25 of 49 voters 
reverse Gore and Nader.  With SSD, Bush voters need at least 25 
order-reversals; truncation will not cut it.

>How can voting randomly require co-ordination?  BTW, sophisticated Bush 
>voters should actually place Nader ahead of Gore in your example.

It requires co-ordination because it will not occur to most voters to flip 
a coin before entering the voting booth.  If the Republican camp says, 
"just vote for Bush" then this will be accepted, and probably not even 
thought of as manipulation.  If they say "flip a coin" or "vote Nader 
second" then there will be a huge stink.

>>>However, if you count ballots in a way that tends to penalize those
>>>who vote partial rankings, which SSD does,
>>
>>I still haven't seen the example that shows this.  [...]
>Your example shows this.  The Bush voters were penalized because they 
>voted partial rankings instead of completing their ballots randomly. Your 
>example stipulates that this is desirable because the incompleteness is 
>strategic.  But the method has no way of knowing people's true preference, 
>so the same effect occurs when the voters are sincere.

My example was aimed at Ranked Pairs, not at SSD.  In Ranked Pairs, the 
Bush camp already succeeds in electing Bush with truncation.  In SSD, they 
would need order-reversal (or random ballots, which is effectively just 
order reversal on half the ballots).

The same effect can occur in a sincere vote, but doesn't it make sense 
then?  You fail to get the desired result because you failed to express a 
true preference.  This is dependent on your second choice losing to your 
first choice pairwise, but beating your third choice by too small a vote total.

>>I've shown an example here where truncation produced a BENEFIT, not a 
>>penalty, with margins.
>No benefit over filling out the ballot randomly, which you can do even if 
>incomplete rankings are banned.

Yes, but does that matter?  My point is that truncation produced a benefit 
over a sincere ranking.  Pointing out that a cleverly completed full ballot 
has the same effect does not change this.

>If you don't express a preference you have, it is natural that this should 
>hurt you as the method can't take that preference into account. But that's 
>not what we are talking about here.

So, are we now talking about the example where I have no preferences other 
than my first choice?  Disregard the immediately following statements if 
this is not the case...

>The point is that if my first choice is A, the method penalizes me for not 
>choosing between B and C, by strengthening one or both candidates, and 
>therefore weakening A.

Certainly not both candidates!  In the zero-information election, you don't 
know which one you should weaken... you may swing the wrong 3-way tie by 
casting an insincere later vote.  It does not seem intuitively obvious to 
me that casting random later votes will generally help you more than it 
hurts you.

In the case where you know the approximate voting profile of the 
electorate, then of course you can pick the later votes on your ballot 
strategically.  A Bush voter in my example who has no sincere second place 
preference would be an example of this.

I guess my point in all of this is that rather than saying "SSD penalizes 
truncation" you could just as easily say "SSD is less vulnerable to 
strategic truncation."  Both can be manipulated to a small degree by a 
smart voter in certain situations.  It sometimes takes a more blatant 
manipulation in SSD than in Ranked Pairs, however.  The fact that most 
differences can be nullified by having random ballot completion does not 
mean things will play out that way in a public election.

Another angle to look at my example from is the case of the 12 Gore voters 
who voted Bush second.  In either method, they make Nader the Condorcet 
winner if the insincerely vote Gore-Nader.  So that's not a good 
option.  But what if those voters simply truncate and vote Gore?  In Ranked 
Pairs, it is largely irrelevant; Bush voters can still win by truncation or 
order reversal (although they now have to be careful not to overshoot with 
order reversal; truncation is safer and easier).  But with SSD, this simple 
truncation guarantees that Bush loses.  All the Bush voters can hope to do 
now by order reversal is mistakenly elect Nader.

This example shows a few interesting points:  One is that the order 
reversal tactic can backfire badly in SSD if the opposing side merely 
truncates in response.  Another point is that truncation does not always 
produce an undesirable result in SSD; in this case it produces a more 
stable favorable result for the 12 Gore-Bush voters than either sincere 
ranking or order reversal would.  It's also worth noting that random ballot 
completion or full preference reversal would not have achieved the same 
stable favorable result.

>When you vote a partial ranking you miss the opportunity to increase the 
>victories between the candidates at the end of your ballot.

But what if you actually change the outcome of one of the victories at the 
end of your ballot?  It is not hard to come up with scenarios where this 
will hurt you.  Indeed, even increasing the victory can hurt you if it 
takes the victory of your end-ballot candidate and makes it larger than 
your favorite's victory.

Again, I do not see the inherent advantage of voting randomly for later 
preferences in the zero-information case.  My example of the 12 Gore-Bush 
voters above illustrates this.

>I don't agree that truncation is that much of a problem, so I am willing 
>to allow incomplete rankings.  But if you disagree, I think that Ranked 
>Pairs with full rankings is a better choice than SSD with partial rankings 
>allowed.

I don't think truncation is a problem either.  I think forced complete 
rankings are a problem.  The two methods are very similar with full 
rankings, and Ranked Pairs is roughly the same with or without full 
rankings.  So the significant comparison is SSD versus Ranked pairs, with 
truncation allowed.

>If I participated in an SSD election, I would feel it necessary to rank 
>all candidates at the end of my ballot, even if I had to vote randomly to 
>do it.  I would advise others to do the same, and I believe I would be 
>giving good advice.

I have already objected to this enough, but let me add one last tidbit: if 
you are confident that a certain candidate is not going to make the Smith 
Set, then there is absolutely no need to rank them in SSD.  So even if your 
random completion is a good tactic in theory, there is no need to continue 
through the Natural Law Party candidate (apologies to any Natural Law folks 
out there).  In ilain Condorcet perhaps, but not SSD.

>Or even worse, they might encourage order reversal, which is a better 
>strategy.  I consider it much more of a threat than truncation.

True, it is a more dangerous strategy.  But in a public election, it is 
less likely to succeed than truncation, due to people's negative reaction 
to it.

>Isn't that the point of your example?  The Bush voters, not understanding 
>SSD, strategically truncate and are thwarted as a result. But if they had 
>understood the method, they would have placed Nader over Gore, or at least 
>voted randomly between them.

Well, my example was not meant to illustrate optimal SSD strategy.  It was 
supposed to be an example of strategic manipulation in Ranked Pairs 
succeeding where it would fail in SSD.  In SSD, the manipulating faction 
would be forced to the more extreme measures you mention to achieve a 
desired result.

>SSD only has a benefit if voters do not understand it.

There is an inherent benefit to method that is more robust against 
manipulation.  If the manipulation has to be more extreme, then it is more 
likely to be well-known in advance, harder to sell to the voters ("I have 
to put Nader second??") and more easily blunted by a strategic reaction 
from another camp.

-Adam