# [EM] TTPBA,TR

C.Benham cbenhamau at yahoo.com.au
Sat Jan 14 17:37:32 PST 2012

```Mike,

> One thing that I like about the tied-at-top methods is that they elect
> A in the ABE,
> meaning that one-sided coalition support is sufficient to defeat C,
> but without giving
> the election away to B.

By the  "ABE", do you mean this?

27: A>B
24: B (sincere is B>A)
49: C

> Of course the election of A violates the Plurality Criterion, but
> that's fine with me.

I wrote in the post suggesting this method that TTBA//TR meets the
Plurality criterion. So does Kevin's ICA method.

In the above example no ballots have any any candidates tied in top
position (i.e. more than one candidate top-rated), so in that case
TTBA//TR is the same as Condorcet//TR (and ICA is the same as
Condorcet//Approval).

http://wiki.electorama.com/wiki/index.php?title=Tied_at_the_top

x: A
1: C=A
1: C=B
x: B

x is any number bigger than 1.  MMPO elects C.

> As currently defined, ICT elects C in Kevin's MMPO bad-example.

No it doesn't.

27: A>B
24: B>C (sincere is B>A)
49: C

> ICT has burial strategy. In the ABE, the B voters can make B win by
> burying A, by middle-
> rating C but not A.

I assume that you are talking about the above example. A candidate that
is not the most top-rated can't win unless its the sole TTBA winner. In
the above example there are no TTBA winners so the
TTBA//TR winner is C

Chris Benham

Mike Ossipoff wrote (14 Jan 2012):

Tied-at-Top-Pairwise-Beats-All, Top Ratings.

In keeping with Kevin's naming, and reflecting its relation to ICA, it
could be called
Improved Condorcet-Top (ICT).

I'll use that because it's shorter.

One thing that I like about the tied-at-top methods is that they elect A
in the ABE,
meaning that one-sided coalition support is sufficient to defeat C, but
without giving
the election away to B.

Of course the election of A violates the Plurality Criterion, but that's
fine with me.
To me, the _practical_ advantage described in the previous paragraph is
worth more than
the non-practical, aesthetic, Plurality Criterion.

ICT has burial strategy. In the ABE, the B voters can make B win by
burying A, by middle-
rating C but not A. Then A doesn't have any indifference on his side, in
hir comparison
with C.

But B still beats C, because B>C is still greater than C>B. For the same
reason, C
still doesn't  beat everyone.

And B still beats A, because
B>A + B=A  is greater than A>B.

So B is now the only beats-all candidate. B wins.

As currently defined, ICT elects C in Kevin's MMPO bad-example.

No one is indifferent between A and B.

So, since A=B is zero, then A>B + A=B is no greater than B>A.

Likewise vice-versa, of course, since A & B are symmetrically-related.

Therefore, neither beats the other.

Maybe that can be fixed, by defining "beat" in the opposite way, so that
x beats y
if x>y is greater than y>x + x=y, and then saying that the winning set
is the set
of unbeaten candidates.

In summary, ICT does three things that some find unacceptable:

1. Plurality Criterion violation
2. Successful burial strategy
3. Noncompliance in Kevin's MMPO bad-example.

#1 and #2 aren't a problem to me. #2 could be, but I don't know what
burial-deterrence
ICT has.

With the sole exception of MMT, the conditional methods meet Mono-Add-Plump.

They probably meet the Plurality Criterion too, because of their close
relation to
Approval. If B defects, those methods elect C, in compliance with the
Plurality Criterion.

Burial strategy has no meaning in the conditional methods. As I've been
saying, they're
a completely new kind of method, with a new kind of strategy, a milder
strategy.

Mike Ossipoff

```