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

[C.Benham]

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