# [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

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

Suppose there is a three candidate MCA race, where all voters submit the

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

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

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

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
point?

Thanks,
Gervase.

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