[EM] The election methods trade-off paradox/impossibility theorems paradox.

[robert bristow-johnson]

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Subject: Re: [EM] The election methods trade-off paradox/impossibility theorems paradox.

From: "Toby Pereira" <tdp201b at yahoo.co.uk>

Date: Sat, June 24, 2017 2:10 pm

To: "rbj at audioimagination.com" <rbj at audioimagination.com>

"election-methods at electorama.com" <election-methods at electorama.com>

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> Given the possibility of a Condorcet paradox, the will of the majority becomes an incoherent notion. If A is preferred by a majority to B, then in a two-candidate election, then A should win under a majority system. But introduce candidate C, and B could end up winning, even though by
majority logic, A is a better candidate than B.
> Obviously you know all about Condorcet paradoxes, but if you think that the majority criterion is some sort of absolute, then you are left with no option but to say that in some elections, A is a better winner than B, B a better winner than C, and C a better winner than A. And this makes no
sense.
of course a cycle is a paradox.  i am also convinced that cycles will be rare.  but they *could* happen on a rare occasion and we need rules set down in advance for how to deal with that contingency.

> You can also end up with winners hardly anyone wants. If there are two polarising candidates each with strong support and a complete unknown, you could have the following ballots:

> 49 voters: A>C>B

> 49 voters: B>C>A

> 2 voters: C>A>B


> It could be that the score ballots (out of 10) would be:

> 49: A=10, C=1, B=0

> 49: B=10, C=1, A=0

> 2: C=2, A=1, B=0



big unrealistic assumptions made here (more likely the 2 voters on the bottom will jack their C preference up to 10 rather than throw away their vote - this is why i am unpersuaded by simulations or hypotheticals dreamed up like this).  how do voters know how to quantify the degree of their
preference?


> C is the Condorcet winner.
as he/she/ should be (ignoring the hypothesized ratings and looking at just the rankings).  it's exaggerated, but this is very similar to the Burlington 2009 election that had a clear Condorcet winner whom was not elected with IRV.  lot's of people,
both Republican on the right and Progressive on the left, felt that the Democrat candidate was an acceptable compromise candidate (and marked their ballots as such) and many (but not enough) Democrats preferred the Democrat candidate over the other two.

> There's no way I'd accept that a C victory is the best result because of blind adherence to some sort of majority principle under all circumstances.
why not?  51% think that C is better than B and 51% think that C is better than A.  

it's a close election, but even if it's close, we still award the victory to the candidate most preferred, even if preferred by a small margin.
>This is not to say that Condorcet methods are necessarily bad, but just that there are elections when they would produce what I would consider to
be the wrong result.
so will IRV.  so will FPTP.  so do multi-winner elections picking the highest "vote-getters".
i presume that Arrow knew what he was writing about.


> And in this situation, very wrong.
nope.



--
r b-j                  rbj at audioimagination.com
"Imagination is more important than knowledge."
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