[EM] MTA vs. MCA (was "An ABE solution")

[Jameson Quinn]

2011/11/21 Chris Benham <cbenhamau at yahoo.com.au>

> "Why ranked and not graded ballots?"
>
> Because
> (a) part of the traditional definition of  ER-Bucklin(whole), aka
> "ABucklin", is that it uses ranked ballots
>
> (b) in some circles/jurisdictions there is no interest in "graded"
> ballots, and there are sometimes more
> candidates than available grades (or rating slots) so ranked ballots allow
> voters who want to stricly rank
> all the candidates to do so, and
>
> (c) if we can use graded ballots then it would be simpler to use
> multi-slot MTA.
>
> MTA stands for "Majority Top,Approval" or "Majority Top//Approval".
>
> But  I agree that these FBC and some of the Condorcet methods run more
> smoothly on grading ballots.
>
> "This method would be consistent with non-normalized ballots (with no
> top-ratings or no bottom-ratings) being
>  strategically optimal in some cases, arguably in most real-world cases."
>
> I don't see how it could be "strategically optimal" to submit a ballot
> "with no top-ratings or no bottom-ratings".
>

I said "in some cases". That is, for some realistic scenarios, if you had
perfect knowledge of other's votes, you still could find no vote that would
be strategically better than your honest, non-normalized vote. In fact,
even if you know that the election is an unknown linear combination of two
(perfectly-known) different election scenarios, your sincere non-normalized
vote could still be optimal.

"Optimal" here means that it is as good as possible. There will always be
an exaggerated and/or normalized vote which is also optimal.

Basically, to make things concrete: in a median-based system, if you know
the two expected frontrunners, and know that both of their scores will be
in a certain grade range, and your sincere scores for those two are outside
of that grade range on opposite sides, then there is no need to further
exaggerate beyond that range. That constraint of course can't hold for all
voters at once (though it will commonly hold for many or most voters); but
there are other cases where exaggeration is pointless, as well as some
voters who don't care about strategy, and so it could be the case that no
strategic voters need exaggerate.

Jameson



> Chris Benham
>
>
>   *From:* Jameson Quinn jameson.quinn at gmail.com
> *Sent:* Tuesday, 22 November 2011 10:53 AM
> *Subject:* Re: [EM] MTA vs. MCA (was "An ABE solution")
>
>  Why ranked and not graded ballots? This method would be consistent with
> non-normalized ballots (with no top-ratings or no bottom-ratings) being
> strategically optimal in some cases, arguably in most real-world cases. As
> Balinski and Laraki argue, using commonly-understood ratings/grades is the
> only way to avoid having strategy be, not just a consideration in rating,
> but the only logically coherent one. And it's easier, cognitively, to
> separately rate each candidate on a meaningful scale than to sort them into
> a rank order.
>
> Jameson
>
> 2011/11/20 C.Benham <cbenhamau at yahoo.com.au>
>
>
> Forest Simmons wrote (17 Nov 2011):
>
> MTA vs. MCA
>
> I like MTA better than MCA because in the case where they differ (two or
> more
> candidates with majorities of top preferences) the MCA decision is made
> only by
> the voters whose ballots already had the effect of getting the ”finalists”
> into
> the final round, while the MTA decision reaches for broader support.
> Because of this, in MTA there is less incentive to top rate a lesser evil.
> If
> you don’t believe the fake polls about how hot the lesser evil is, you can
> take
> a wait and see attitude by voting her in the middle slot. If it turns out
> that
> she did end up as a finalist (against the greater evil) then your ballot
> will
> give her full support in the final round.
>
> <end Forest quote>
>
> I buy this. I agree that MTA is a bit better than MCA. Well done Mike.
>
> * Voters submit 3-slot ratings ballots, default rating is Bottom
> signifying least
> preferred and not approved. Top-rating signifies most preferred and
> approved.
> Middle-rating also signifies approval.
>
> If any candidates are Top-rated on more than half the ballots, elect the
> one of
> these with the most approval.
>
> Otherwise elect the most approved candidate.*
>
> A slight marketing problem could be that the difference between this and
> MCA
> (and also between those and a third possible similar method: the TR winner
> wins if
> s/he has majority approval, otherwise the most approved candidate wins)
> could
> to some members of the public appear to be quite arbitrary and unimportant.
>
> Also of course MTA is little bit more complex to count than MCA. But on
> the positive
> side, it has just occurred to me that it would work better than MCA
> extended to using
> 4-slot ballots (with as with 3 slots, any rating above the bottom-most
> slot is interpreted
> as approval).
>
> I suppose by the same reasoning we could improve ER-Bucklin(whole), which
> has
> been given the briefer and quite apt new name by Mike O. of "ABucklin".
>
> My stab at defining the so improved version:
>
> *Voters submit ranking ballots, equal-ranking and truncation allowed.
> Ranked (i.e.not
> truncated) candidates are considered to be approved.
>
> Rankings are interpreted as ratings thus: candidates ranked below no
> others are in the top
> ratings slot. Those with x candidates ranked above them are in (x-1)th.
> ratings slot from
> the top. (So A=B>D is interpreted as A and B in top slot, second-highest
> slot empty,
> D in third-highest slot).
>
> Say the ratings slots are labelled from highest (signifying most
> preferred) down as alphabetical
> grades A, B, C, D etc.
>
> If any candidates are graded A on more than half the ballots then elect
> the most approved one
> of these.
>
> Otherwise if any candidates are graded A or B on more than half the
> ballots then elect the most
> approved one of these.
>
> Otherwise if any candidates are graded A or B or C on more than half the
> ballots then elect the
> most approved one of these.
>
> Continue in this vein considering the next lowest grade each round until
> there is a winner, or if
> that fails then elect the most approved candidate.*
>
> I think IBIFA is still quite a lot better than any of these methods, but
> it is more complicated.
> IBIFA has a less strong truncation incentive and the IBIFA winner will
> never be pairwise-beaten
> by the winner of any of these methods.
>
> Chris Benham
>
>
>
>
>
>
>
>
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