[EM] Advantages of CR style ballots

[Forest Simmons]

Joe Weinstein argues the advantages of unconstrained CR style ballots
below.  I would like to add my two bits worth.

Most of the arguments against the use of CR ballots are based on the
misguided assumption that the only way to use CR ballots is to give the
win to the candidate with the highest average rating.

That assumption is tantamount to believing that the only way to use ranked
ballots is to give the win to the candidate with the highest average rank
(the Borda winner).

Note that CR ballots can be used for head-to-head comparisons
(generalizing Condorcet methods).

CR ballots can be used to find the candidate with the highest median
rating (generalizing Bucklin). 

There are many other uses of CR ballots.  Lorrie Cranor uses CR ballots
as input for her Declared Strategy Voting (DSV) methods.

All of these uses of unconstrained CR ballots allow the voter more freedom
of expression than the constrained methods that use the same information
capacity ballot.

Constraints tend to limit the information efficiency of the ballot.

For example, the lone mark plurality ballot can be used for Approval if
the constraint is removed.

Another example:

Three bits of information are required to distinguish among five
candidates, so a ballot that allows the voter to rank five candidates
requires making at least a three bit mark beside each candidate's name.
Without the constraint, the same ballot could be used to rate each
candidate on a scale of zero through seven.

More commonly five bit codes are used to rank five candidates (five
distinct bubbles to the right of each candidate).  The same ballot could
be used to rate each candidate on a scale of zero to 31.

Furthermore, the lack of constraint makes it harder for a voter to foul
the ballot. In other words, a voter can hardly violate non-existent
constraints.  Which is harder to mess up ... lone mark or Approval?  A
lone mark voter who doesn't notice the (rather ridiculous) "one mark only"
instruction can accidently foul his ballot if he likes two of the
candidates.

Forest


On Thu, 27 Dec 2001, Joe Weinstein wrote:

> 
> 
> 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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