[EM] majoritarian top ratings (MTR)

[Chris Benham]

Kevin Venzke wrote:

>Hello,
>
>My favorite method lately I'll call "majoritarian top ratings" or "MTR."
>I don't believe it has been suggested on the list. Here is the definition:
>
>1. The voter gives every candidate the "top" rating, the "middle" rating,
>or no rating at all, which is the bottom rating.
>
>2. Say that a candidate X is "defeated by a majority" if more than half
>of all voters assign some other candidate Y a strictly higher ranking
>than they assign to X.
>
>3. Elect the top candidate in the ordering of candidates wherein a 
>candidate X is above candidate Y when X is not defeated by a majority
>while Y is, or (when this makes no distinction) when X received the top
>rating on more ballots than did Y.
>  
>
Kevin,
Is there some reason apart from simplicity that you use MDD instead of  
CDTT?

5:A>B
5:B>C
5:C>A
3:D>A
3:D>B
3:D>C

All except D has a majority-strength defeat, but D is pairwise beaten 
10-9 by every other
candidate.

CDTT  can't be just the Condorcet loser, as the MDD set is here.

>Advantages of this:
>1. FBC
>2. (my interpretation of) minimal defense
>3. limited later-no-harm, in that you can't hurt your top-rated candidates
>by listing middle-rated candidates.
>
I suppose you can add the "3-slot versions" of  Smith(Gross) and  
Majority for Solid Coalitions.

>Disadvantages:
>1. fails Plurality (although not as egregiously as MMPO)
>2. potential for burial strategy (although with the usual countermeasures)
>  
>

Take the 0-info. voters whose main or only preference is between candidates 
they regard as acceptable and all the others they regard as unacceptable
(i.e. they have one big gap in their sincere ratings). For them the sincere
way of voting would be to ignore the middle slot and just submit an approval 
vote, putting all the unacceptables in the bottom slot.

But in fact their best strategy is to randomly select half the unacceptables
and put them in the middle slot, maybe causing one that would otherwise beat
an acceptable candidate to be disqualified.

With information, the middle slot would mainly become a cynical strategy-tool
for factions to try to disqualify the most electible candidate/s in rival 
faction/s. The effect of that could be the election of a "turkey" with little
sincere support.

MTR of course fails Independence from Irrelevant Ballots (IIB), and also 
Clone-Winner (unless the defence "but these are ratings ballots, and a set of
clones must by definition share the same rating" is invoked).

25: A>B
23: B>A
45: C
07: D

C wins, but if the "irrelevant" 7D ballots are removed then A wins.

If instead one of the {A,B} "clones" are removed then the other will win (i.e. if
the clone-set is replaced by a single candidate X which is "top-rated" by all those
who voted A>B or B>A, then X will win).

It seems to me that FBC/SF compliance is just so "expensive" and to me uninspiring
and "negative minded". My favourite 3-slot method definitely remains "3-slot DMC".
FBC complying methods generally at least verge on being strategically equivalent
to plain Approval (in the case of MTR, with extra burial opportunities and a random-fill
incentive).


Chris Benham