[EM] MCA cut off points arbitrary? [Was: Hello (Intro); PR, Condorcet and Approval, variants...]

Gervase Lam gervase at group.force9.co.uk
Tue Feb 25 16:05:19 PST 2003

> I would say that
> the "majority" criterion in other systems (plurality
> w/ run-off, IRV, Majority Choice Approval) is a shade
> arbitrary.

> Stepjak

I can make two arguments about MCA's arbitrariness.

A one candidate Approval vote is like saying yes or no to choosing the 
candidate.  However, there is a region between the no (0% = 0) and the yes 
(100% = 1).  You either vote the candidate in (1) or not (0).

In other words, it's a like an analogue to digital system.  The analogue 
signal needs to converted to a 1 bit number.

For such a A-to-D system, where should the cut off point be?  Right in 
between the 0 and 1.  0.5, that is.

Now back a bit to MCA.  MCA has Favored, Compromise and Unapproved. 
 If the Compromise level were removed, all that would remain is Favored 
and Unapproved.  In other words, just ordinary Approval.

There is the argument that only the candidate(s) that get a yes from the 
"A-to-D" system should win.  That means only candidate(s) with more than 
50% Favored should win.  Obviously, there would need to be more steps if 
none of the candidates got more than 50% of the Favored votes and a 
candidate had to be chosen.

However, I've been wondering whether one candidate 'trumps' all of the 
other candidates if the candidate was the only one that got greater than 
50% of the Favored votes.

Suppose there is a three candidate MCA race, where all voters submit the 
following sincere votes:

51 ABC
49 BCA

Using 50% as the percentage Favored votes required for a win, A would win 
with MCA.

However, it would be natural to assume that the opposite of Favored is 
Unapproved.  That is, MCA has levels that are like a 3-level Cardinal 
Ratings system with each Favored vote getting +1 and each Unapproved vote 
getting -1.  Therefore, each Compromise vote should get 0.  Using this, B 
would be the winner.

For A, the 49 Unapproved votes cancels out virtually all of the 51 
Favored votes.  For B, none of the 49 Favored votes is cancelled out.  
(Interestingly, A is the Condorcet Winner in this race.)

So, what is the Favored win percentage that is required to "trump" the 
other candidates?

67 ABC
33 BCA

Nett favored votes:

A: 67 - 33 = 34
B: 33 - 0  = 33
C:  0 - 67 = -67

In other words, 2/3 of the votes must be Favored votes.

It seems to me that 2/3 could be a hard target to reach.  After all, 
it is only 10% (a tenth) away from 75% (3/4).  Therefore, voters and 
possibly candidates might not think too much about Favored votes.

Admittedly, these two examples are only three candidate cases.  With more 
candidates, candidates would be given joint "levels."  The likelihood of 
more than one candidate getting 2/3 of the Favored votes would increase.

However, in an MCA race with more than three candidates, how would voters 
vote?  How should voters vote given that each voter would have their own 
utilities for each candidate?  In other words, quantitatively, where is 
the cut off point between Favored and Compromise?  Where is the cut off 
point between Compromise and Unapproved?  Could these cut off points be 
positioned fairly by choosing the correct Favored vote percentage/cut off 


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