[EM] Fw: MJ better than IRV & MAM

[Kristofer Munsterhjelm]

On 07/13/2016 07:47 AM, steve bosworth wrote:

> K:  As for the MAM example, it seems that F wins in MAM as well.
> 
> S:  Yes, F does win with MAM. I clearly made a mistake when counting. 
> However, I believe the following new profile does illustrate the point I
> was trying to make (see below).  This is that MAM (or any Condorcet
> method) is less efficient than IRV in discovering the winner with the
> highest available average intensity of majority support.  This is
> because MAM does not count the different intensities of preference as
> illustrated by the following calculations:  If each of the ordinal
> preferences within this profile receive a score out of 10, 10 being
> given to each 1^st choice, F receives an average intensity of support of
> 9.1 from the majority of 70 that elects her, or 8.47 from all 100 voters.
> 
> This contrasts with N who is elected both by MAM and Majority Judgment
> (MJ).  N’s average intensity of support from all 100voters is 7.51. 
> More exactly MJ elects N because she has received the highest
> ‘majority-grade’ of GOOD (i.e. perhaps this corresponds to a score of 8).

[snip]

> *PROFILE: A BETER EXAMPLE:*
> 100 CITIZENS RANK CANDIDATES EFGKMNP AS FOLLOWS:

I've restated that example into the standard ranked ballot format:

49: F>P>K>N
30: M>E>N>F
21: G>K>N>F

And Eric Gorr's MAM implementation http://www.ericgorr.net/condorcet/

says that F wins under MAM ("Ranked Pairs (Deterministic #1-Winning
Votes)") as well[1].

According to LeGrand's voting calculator,
http://www.cs.wustl.edu/~legrand/rbvote/calc.html

the only methods (among those implemented there) that make N win are
Copeland (with random tiebreak), Raynaud (ditto), and Small. Note that
LeGrand's calculator uses margins, so the defeats matrix will look
different.

I haven't checked your majority figures yet as I'm not feeling all that
well today. I haven't checked your MJ result either; but a very quick
and dirty Bucklin count seems to support that N would win under MJ.

I would also like to again mention that one can construct examples where
IRV does worse by your intensity calculations. I gave one such example
in a previous post, and here's another from
http://rangevoting.org/CoreSuppPocket.html:

35:A>C>D>B
17:B>C>D>A
32:C>D>B>A
16:D>B>C>A

IRV elects B. MAM elects C. Say first preferences are 10 points, second
is 9, third is 8, and fourth is 7, then

B has an intensity of

(35 * 7 + 17 * 10 + 32 * 8 + 16 * 9) / 100 = 8.15

while C has an intensity of

(35 * 9 + 17 * 9 + 32 * 10 + 16 * 8) / 100 = 9.16.

Come to think of it, any center squeeze example would do. Here's LCR:

48: L>C>R
32: R>C>L
20: C>R>L

IRV elects R while every Condorcet method (and Bucklin/MJ) elects C.

C's intensity is: (9 * 48 + 9 * 32 + 10 * 20)/100 = 9.2
R's intensity is: (8 * 48 + 10 * 32 + 9 * 20)/100 = 8.84.

-

[1] It's not strictly speaking MAM because MAM handles ties among
majorities differently, but I don't think breaking ties differently
would make N win.