[EM] EQTOP-MPO MAMPO example

[Forest W Simmons]

I never claimed that EQTOP-MPO satisfied any strategy free criteria.  
To the contrary I pointed out the drawback that it requires approval 
style strategy even in the zero info case.

That method was just the introduction to a better method that 
immediately followed it in the same message.

Here's the improved version of PG-MPO (for want of a better name):

Ballots are range style.

For each candidate X and each range level R, let A(X,R) be the number 
of ballots on which X is rated at level R or above.

Let B(X,R) be the greatest number of ballots on which any one candidate 
is rated above X while X is rated below R (hence PG).  In other words, 
B(X,R) is the max pairwise opposition for X when all ratings above R 
are collapsed to level R.

Let R be the highest range level for which there is a candidate X for 
which the difference A(X,R)-B(X,R) is positive.

Elect the candidate X with the largest such difference at that level R.

Since Mike's example did not include ratings, this method cannot be 
applied to it.

Forest




Mike O. wrote ...

>
>Forest--
>
>Example with EQTOP - MPO MAMPO:
>
>1000 voters:
>
>380: AB
>124: B
>124: CB
>124: DB
>124: EB
>124: FB
>
>It’s obvious that this example is a failure example for EQTOP-MPO MAMPO 
with 
>the votes-only counterparts of SFC and SDSC. But I’ll demonstrate that 
>obvious fact anyway, at the end of this message.
>
>Note that, in this example, the A voters aren’t even truncating or 
using any 
>kind of offensive strategy.
>That suggests that Steve Eppley’s name for votes-only SFC 
>(“Truncation-Resistance“) isn’t general enough.
>Likewise, the well-known IRV fails without truncation or any offensive 
>strategy.
>
>By the way, it was Steve Eppley who first proposed the votes-only 
>counterpart to SFC. I didn’t like it because (as I discussed yesterday) 
it 
>doesn’t tell the important guarantee of SFC that I want to tell. It’s 
lack 
>of applicability to all methods is another reason to not accept is as a 
>replacement for SFC.
>
>If people would prefer, I’ll use the votes-only counterparts of SFC and 
>SDSC, when evaluating rank methods (but not when comparing them to 
nonrank 
>methods). I do so with the understanding that my preference versions 
are the 
>actual criteria, and the votes-only versions are only a convenience,  
when 
>comparingrank methods to eachother.
>
>I’ll do that because it’s true that my preference criteria are a little 
less 
>convenient for rank methods. And they require information, preferences, 
that 
>needn’t be involved when comparing  rank methods to each other.. And we 
all 
>know that only rank methods are going to pass SFC and SDSC anyway.  For 
that 
>reason the preference versions  could even be called “inelegant”, when 
>comparing only rank methods.
>
>But, when it’s necessary to evaluate or compare to nonrank methods, the 
>elegance comparison between votes-only and preference is reversed. 
Then, the 
>preference criteria are the ones that are elegant, because of their 
uniform 
>applicability to all methods.
>
>When comparing all methods, there’s nothing elegant or convenient about 
the 
>votes-only criteria, and their use of FARCS. In fact, “votes-only” 
loses its 
>meaning when FARCS calls “intended rankings” (which can’t even really 
be 
>intended) “votes”.
>
>Of course here’s why the example is a failure example for EQTOP - MPO 
MAMPO, 
>with votes-only SFC & SDSC:
>
>A majority rank B over A, but no majority rank anyone over B. But A 
wins.
>
>A majority rank B over A, and don’t rank A. But A wins.
>
>For applying the preference SFC and SDSC, it would be necessary to 
state 
>preferences, and to make the rankings of the {B,C,D,E,F} voters 
complete, to 
>satisfy the sincerity requirement of SFC. But EQTOP-MPO MAMPO fails 
>preference SFC and SDSC too.
>
>
>Mike Ossipoff