[EM] "Turkey" problem and MCA

[Gervase Lam]

> Date: Wed, 28 May 2003 20:05:10 +0200 (CEST)
> From: =?iso-8859-1?q?Kevin=20Venzke?= <stepjak at yahoo.fr>
> Subject: Re: [EM] "Turkey" problem and MCA
> To: election-methods at electorama.com

> > > 48: A>B>C  (A worth 100, B worth 15, C worth 0)
> > > 2: B (B worth 100, A and C worth 0)
> > > 48: C>B>A  (C worth 100, B worth 15, A worth 0)

> (Imagine that both A and C are shy of a majority.  It's not too late
> for Favorite to win.  But he WILL lose if his supporters approve B.)
> There is not enough gain for the risk, to approve B.

Wow!  You're right.  This is very good in this situation because the 
voters would vote according to the approximate Sincere Utilities/Worths 
that are against each MCA level:

< 50% => Disapprove
> 75% => Favourite
Other => Approve (i.e. cut-off for Disapprove has already been determined, 
so get the cut-off between Favourite and Approve).

> >  Would
> > the voters use Approval strategy if normal Approval were used?  If so,
> > they might do the same thing and vote for B as well as their favorite.
> >  It really depends on what type of "Approval" strategy the voters in
> > MCA and normal Approval use.

Sorry.  I rushed this paragraph a bit as it was late (Not that it is not 
late right now!).  I pondered whether I should refer to the recent post 
that Adam Tarr did on 26th April 2003 that clarified the main simple 
Approval strategy.  I should have.

It is possible to come up with better strategies.  I think Mike Ossipoff 
came up or tried to come up with a strategy that used win 
probabilities/odds of each candidate to get the strategy.  I think the 
overall feeling about this type of thing is that there is little gain for 
a lot of effort.

> The voters shouldn't approve B in plain Approval.  Pretty sure about
> that. Their votes stand to gain them less if they do.

In addition to the main strategy, Adam also mentioned in the post: "If the 
election is a dead heat between two frontrunners, the best strategy is to 
approve candidates that you like more than the average of the two 
frontrunners."

> I bet it wouldn't be too hard to come up with the ideal strategies for
> MCA.  More odds would have to be estimated, though, such as "perceived
> odds of X getting a majority of Favorite rankings."
>
> Actually, you go a long way if you can estimate "perceived odds of
> NOBODY having a majority of Favorite rankings."  In that event
> Favorite/Approved makes no difference.

In other words, it's then just straight Approval.

In the case of estimating the odds in the first paragraph, I thought that 
it would be reasonable to assume that Approved/Disapproved are no 
different to each other.  So therefore you have another straight Approval 
situation.  Obviously this depends on the odds.

Forest sent a couple enlightening posts that mentioned about the 
odds/probabilities in straight Approval on 19th April 2003 given a race 
with two front runners or a random distribution of utilities/worths.  I'll 
see if I can get my poor brain to adapt these to MCA.

> How would more slots change MCA?  That's an interesting question.  It
> seems to me that you would create a more obvious game of Chicken.  As
> MCA already is, it's not "safe" to put candidates in the 2nd rank,
> because your 1st rank candidate could still win.  You hope that other
> voters put your 1st rank candidates in their own 2nd ranks.  In
> other words, you want to withhold your concessions if you can.
>
> I'd bet that if you had five-rank MCA, the 2nd and 3rd ranks would
> often be unused.  I'll ponder that, too.

I indirectly mentioned this in my recent "MCA and median" posts.  
Basically, the posts said that the MCA winner was the candidate with the 
highest median, disregarding any tie-breakers required if more than one 
candidate gets the highest median.

In the resulting thread, I also mentioned the MCA theory that very 
basically said that the only time you need to up-rate a candidate to 
Favourite is if one of your Disapproved candidates was going to tally over 
50% of the Favourite votes (i.e. the candidate you disapproved of has a 
median of Favourite).  In other words, "if you can't beat them, join them 
or better them."  With "3-rank" MCA, you can't really better a candidate 
who has a median of Favourite.

However, if after a "4-rank" MCA vote, the highest median is found to be 
the 2nd from top rank and this is the median rank of one of your bottom 
ranked candidates, you can give what you think is a better candidate a 
better rank than this median, not just equal that rank.

This possibility seems to make things complicated if you have several 
candidates you consider to be bottom ranked who have medians equal to 
either of the 2 middle ranks.  This means that you'll have to 
appropriately rank the better candidates above the bottom ranked 
candidates' medians as well as ranking the better candidates in relation 
to each in a similar fashion.

That's why I think MCA shouldn't really go beyond 3 ranks.  At least, 
that's what I think at the moment.

Thanks,
Gervase.