[EM] FBC ambiguity?

[Joe Weinstein]

Just about every 1-winner method which avoids actual physical runoff amounts 
to a form of CR (cardinal ratings), in which the voter may assign each 
candidate an integer-valued grade in all or a given part of the range 0 
through M, where M is the method's max-allowed grade.

With pure CR, candidates may be independently ranked: reranking of one 
candidate never forces reranking of another.

However, many commonly discussed methods amount to CR with extra constraints 
on a valid marked ballot's allowed combinations of ratings of different 
candidates.  Two such kinds of constraints are very common. A 'cumulative' 
method - such as the usual Lone-mark plurality (M=1) - puts a cap on allowed 
cumulated sum of ratings. (The pure case M=1 and no extra constraint amounts 
to Approval; with a constrained cap of 1, the method becomes Lone-mark.) 
Other methods - notably usual Borda and IRV - require that nonzero ratings 
of distinct candidates be unequal.

I have yet to see any good arguments for such extra constraints. They serve 
just to introduce problems which interfere with and subvert expression of 
legitimate sentiments and widely preferred and preferable outcomes. For 
instance, widely preferred candidates who are 'clones' or 'quasi-clones' are 
gratuitously pitted against one another.

Another such problem emerges from recent EM-list postings. On Th 27 Dec 
2001, Mike Ossipoff wrote:

     "Richard [stated that Forest and he] had an off-list discussion some 
time ago about defining monotonicity, and the prerequisite definition of 
"changing a ballot in a way that favors candidate X". Making such a 
definition generally applicable (beyond fully ranked methods) is trickier 
than one would think. For instance, in CR, if candidate X's rating is 
increased from 25 to 30, does this favor X? Yes, but what if candidate Y's 
rating is increased by 10 points at the same time X's rating is increased? 
We never came up with a completely satisfactory resolution...

     "I too have noticed that wording Monotonicity precisely is trickier 
than one might at first expect. But I think it's reasonable to assume that 
when we refer to changing X's rating, that doesn't include changing someone 
else's rating too..."

Mike is right: it IS reasonable to assume that when we refer to changing X's 
rating, that doesn't include changing someone else's rating too.

However, reasonable or not, given ANY method with extra constraints, in some 
situations a desired change of X's rating will FORCE us to change someone 
else's rating - in order to keep the ballot validly marked for that method.  
For instance, with Lone-mark 'plurality', if we start with a ballot which 
rates candidate X as 0 (NO) and candidate Y as 1 (YES), we may rerate X as 1 
but ONLY if we also rerate Y as 0.

Contrary to what the above quote hints, a method may be 'fully ranked' and 
yet still manifest this problem. On the other hand, also contrary to what 
the above quote hints, it is precisely the pure (unconstrained) CR methods 
(including Approval) which do NOT ever have this forced reranking problem.

Joe Weinstein
Long Beach CA USA

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