[EM] Majority Judgment avoids Arrow's Theorem (paradox)

[steve bosworth]

Is it not still true that one of the great virtues of MJ is that it avoids Arrow's paradox?


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Subject: Election-Methods Digest, Vol 155, Issue 21


1. Corollary to Arrow's Theorem (Rob Lanphier)
2. Re: Corollary to Arrow's Theorem (Juho Laatu)


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Date: Wed, 31 May 2017 08:50:52 -0700
From: Rob Lanphier <***@robla.net>
To: election-***@lists.electorama.com
Subject: [EM] Corollary to Arrow's Theorem
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Hi all,

It appears that Randall Monroe has discovered an important corollary to
Arrow's Theorem. It takes some patience to sort through it, but you'll
find it described in this paper:
<https://xkcd.com/1844/>


Something to think about.

Rob------------------------------

End of Election-Methods Digest, Vol 155, Issue 21
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[f***@snkmail.com]

Arrow's theorem only applies to ranked systems, while MJ is a rated system
(as are Score/Range, SRV/STAR, Approval, etc.) Later in life, Arrow
supported rated systems: https://electology.org/
podcasts/2012-10-06_kenneth_arrow

Gibbard's theorem is supposed to apply to all conceivable voting systems,
though.

On Mon, Jun 5, 2017 at 5:48 PM, steve bosworth stevebosworth-at-hotmail.com

Post by steve bosworth
Is it not still true that one of the great virtues of MJ is that it avoids Arrow's paradox?
------------------------------
*Sent:* Wednesday, May 31, 2017 7:03 PM
*Subject:* Election-Methods Digest, Vol 155, Issue 21
1. Corollary to Arrow's Theorem (Rob Lanphier)
2. Re: Corollary to Arrow's Theorem (Juho Laatu)
----------------------------------------------------------------------
Message: 1
Date: Wed, 31 May 2017 08:50:52 -0700
Subject: [EM] Corollary to Arrow's Theorem
ail.com>
Content-Type: text/plain; charset="utf-8"
Hi all,
It appears that Randall Monroe has discovered an important corollary to
Arrow's Theorem. It takes some patience to sort through it, but you'll
<https://xkcd.com/1844/>
Something to think about.
Rob------------------------------
End of Election-Methods Digest, Vol 155, Issue 21
*************************************************
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[Kristofer Munsterhjelm]

Post by f***@snkmail.com
Arrow's theorem only applies to ranked systems, while MJ is a rated
system (as are Score/Range, SRV/STAR, Approval, etc.) Later in life,
https://electology.org/podcasts/2012-10-06_kenneth_arrow
<https://electology.org/podcasts/2012-10-06_kenneth_arrow>
Gibbard's theorem is supposed to apply to all conceivable voting
systems, though.

Just to be precise, to all conceivable _deterministic_ voting systems.
Any random method of the type:

- With probability x%, choose the Random Ballot winner,
- With probability (100-x)%, choose the Random Pair winner

is strategyproof. It's also not very good.

To be even more precise, Random Winner is also strategyproof as far as
strategy from the voters is concerned, because the ballots are never
looked at. It has an obvious teaming strategy, however. And dictatorial
systems are strategyproof, but lacking for other reasons.
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[Juho Laatu]

I just note that one could try nomination strategies / teaming also in Random Pair (e.g. 100 republican candidates against 1 democrat).

BR, Juho

Post by Kristofer Munsterhjelm

Post by f***@snkmail.com
Arrow's theorem only applies to ranked systems, while MJ is a rated
system (as are Score/Range, SRV/STAR, Approval, etc.) Later in life,
https://electology.org/podcasts/2012-10-06_kenneth_arrow
<https://electology.org/podcasts/2012-10-06_kenneth_arrow>
Gibbard's theorem is supposed to apply to all conceivable voting
systems, though.

- With probability x%, choose the Random Ballot winner,
- With probability (100-x)%, choose the Random Pair winner
is strategyproof. It's also not very good.
To be even more precise, Random Winner is also strategyproof as far as strategy from the voters is concerned, because the ballots are never looked at. It has an obvious teaming strategy, however. And dictatorial systems are strategyproof, but lacking for other reasons.
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