[EM] 09/20/02 - The Manipulation Test:

[Adam Tarr]

Donald Davison wrote:

>Mike Saari: "Suppose there are only two candidates, or suppose that all
>candidates have been eliminated down to only two.
>
>Here is the sample scenario:
>All of the voters rate candidate "B" as "very good".
>60% of the voters rate candidate "A" as "excellent"
>The other 40% of the voters rate candidate "A" as "awful".
>
>Donald: Candidate A is the winner.  I'm telling you that right up front.  I
>don't need to hear a bunch of twisted logic to the contrary.

Don, you're pretty much right.  What's more, you're right regardless of the 
voting system.  I mean, we're talking about two candidates here.  It's not 
complicated.  Regardless of what the voting system is, you just vote for 
the candidate you like more.  This applies to approval voting too.  I mean 
really, do you expect that an "A" supporter would walk into the voting 
booth and vote for BOTH available candidates?  They may as well just stay 
home and watch Baywatch reruns.

Even if Mike Saari gravitates toward approval voting, his proposed election 
gives the same result with approval voting as it does with any other 
deterministic voting method.

>Mike Saari: "So which candidate is the "better" choice - the one liked by
>everybody, or the one hated by 40% of the group?"
>
>Donald:  Answer: Candidate `A'.  See I told you you're not going to get
>from me the answer you are looking for.

Here I disagree with you.  In a perfect world, "B" wins the election, and 
everyone is fairly content.  But we don't live in a perfect world.  The "A" 
supporters have a majority, so they get what they want, even though they 
are aware that they could live with "B".  This is true no matter what 
voting system we choose.

Now, I can come up with a couple situations where approval voting, and its 
sibling cardinal rankings, will elect a "B"-type candidate over an "A"-type 
candidate.  But these situations will have two things in common:

1)  The voters don't know the numbers of the current polls with any accuracy.
2)  There is a third, disliked option that scares the A voters into voting 
for B.

For example, let's say in stead of 60% "A" and 40% "B", we have 45% "A" 30% 
"B", and 25% "C".  The A and B voters all hate C, and the C voters have no 
preference between A and B.

In plurality, IRV, or Condorcet, A still wins the election.  This is also 
true in approval voting or cardinal rankings if the voters know the poll 
numbers.  But if the "A" voters are in the dark about the poll numbers, 
they may approve B as well to protect from C.  If that happens, then B wins 
the election.

>Mike Saari: "Such a belief is unfounded, though, if you realize that this
>method creates a "40% are unhappy" group, whereas a system with some
>possibility to choose the less "exciting" (but liked by all) candidate B
>creates a group which is more contented overall."

Short of plugging every voter into a polygraph and interrogating them, we 
have no way to figure out exactly how much more the voter likes one 
candidate as compared to the next.  Expecting voters to act against self 
interest because it maximizes overall social utility is a losing battle.

>Donald:  If this is the best argument you can present for Approval Voting,
>then you lose, because almost everyone wants their own number one to win.
>The Approval supporters are fools to think Nader would have won if the last
>Presidential election was an Approval Voting election.

I don't think anybody seriously thinks that.  Is that last line anything 
but a pot shot at greens who support approval voting?

Anyway, this is not the best argument for approval voting in my book, 
although it is a subset of one decent argument for approval - that voters 
can produce very good results even if the media covering the election gives 
unreliable information.

-Adam


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