[EM] uses of truncation

Abd ul-Rahman Lomax abd at lomaxdesign.com
Mon Mar 19 21:25:27 PDT 2007

At 03:20 AM 3/17/2007, Dave Ketchum wrote:
>Offer me true Approval - the one that differs from Plurality only in 
>permitting over votes - and we have something understandable and, 
>occasionally, useful.

This is true Approval. What else would it be?

(Ballot design may vary, but the essence is that you may vote for one 
or more candidates, and the candidate with the most votes wins.

>Offer me Range and we are, presumably into something else:
>      I need to understand its abilities and method of invocation, 
> to decide if I wish to use such.

Sure. There are variables, and Range advocates are not unanimous 
about the best method of implementation. The basic idea is simple: 
voters may assign a score or rating in a range of allowable scores. 
It is generally assumed that this range is linear and integral, i.e., 
the scores are of the form of N, N+1, N+2, ..., R-1, where the method 
is Range R, and N is often assumed to be zero. Thus Approval is Range 2.

There are two methods of determining the overall score for 
candidates: summation and averaging. If everyone assigns a score to 
every candidate, summation and averaging provide the same relative 
results. However, because Range can be implemented on standard voting 
equipment, as if each candidate were a race (i.e., a multiple choice 
list), it is possible to amalgamate the scores by averaging.

As has been noted, Approval Voting is effectively used for choosing 
between multiple conflicting ballot initiatives, where, should both 
initiatives pass, the one with the most Yes votes wins. This would be 
summation Range 2. Average Range 2 would compare the Yes/No ratios 
for the two "candidates."

Personally, I find that using Average Range, while it has some 
attractive features, introduces far too much complication, for it 
becomes necessary then to introduce what CRV calls a "quorum rule," 
limiting the conditions under which a dark horse candidate, one rated 
by relatively few, can win. So my own basic Range proposals would be 
summation Range; the result is that blank votes are counted 
effectively as if they were minimum rating. There is another 
possibility, to be sure:

If the Range is -1, 0, +1, which has been suggested by a number of 
writers, including myself, then blank votes would be counted as an 
intermediate vote....

My own preference is to go for simple Approval first, because 
implementation is extremely simple -- it is actually easier to count, 
in some ways, than standard Plurality, and to then work on where to 
go from there. Approval resolves the first-order spoiler effect. 
Certainly Approval does not allow great flexibility of expression, it 
is merely a drastic improvement over standard Plurality.

(It is, in fact, what standard Plurality would be if not for the 
special no-overvoting rules that seem to be ubiquitous, though only 
where paper or equivalent ballots are used. No-overvoting is never 
enforced when voice vote is involved, nor with show of hands, only 
where there is a roll call or secret ballot.)

>      My desires often remain with Plurality.  Is there a way to 
> express that thought under Range?  Do I have the same power that I 
> would have under Plurality or Approval?

Yes, you have the same power. Just vote max rating for one candidate. 
If it is summation Range, you are done. If it is average Range, then 
you may have to rate all candidates or lose voting power. Range 
advocates generally do seem to want to provide a means that voters 
can indicate something like "Treat my blanks as zero rating," or they 
will add an Abstain option. If you don't check the Abstain option, 
you have voted a zero rating.

I think that this could be an example of the Best is the enemy of the 
Good. While it seems reasonable to allow voters to explicitly 
abstain, it complicates the ballot and it is speculative what social 
benefit is obtained. Once we have Approval, we may then have Range 
with N > 2. And we can then consider what to do with abstentions. The 
tradition, based on the procedure with ballot initiatives, is that 
abstentions are equivalent to No, for the purpose of comparing two 
initiatives. (If you *really* want to abstain in a race, you simply 
don't vote for anyone, you then will not affect the outcome at all.)

>Point is that you complicate life for me, i.m.voter.  You claim to 
>offer value for the cost - something to debate another day.

Approval doesn't complicate things for you at all, and a decent Range 
ballot wouldn't either. A great deal depends on ballot design and 
instructions. Actually voting Range in a manner equivalent to 
Plurality is trivial, as I mentioned: just max rate your favorite and 
zero everyone else. Range voters should understand that any vote 
other than max or min is a "weak" vote. That is, it has an intermediate effect.

One way of looking at Range N is that you have N-1 votes to cast. 
Cast as many as you like, up to N-1, for as many candidates as you 
like. Obviously, if you cast your votes equally for all candidates, 
it is as if you stayed home, in one way. Or it could mean that you 
truly are equally satisfied with all. If you don't cast all your 
votes, you are weakening your vote. It's up to you if you want to do this.

Voting strategy can get complicated, but only a way that is also true 
for Plurality: you may wish to consider not only your own "favorite," 
but also how other voters are likely to vote. If your Favorite is not 
likely to win, you will waste your vote by only voting max for your 
favorite and min for everyone else. You may quite reasonably vote 
Range Approval style, that is, select an approved set and vote max 
for all of them and min for everyone else.

More likely, I think, voters will vote min for anyone you consider a 
truly bad choice for the office. And they will certainly vote max for 
their favorite, and maybe, under some conditions, for another -- 
typically the favorite among the top two -- and then some 
intermediate votes for candidates that the voter wishes to express 
some support for.

It's not completely clear how voters will choose to vote. However, 
what is clear is that the only way that Range makes it more 
complicated is if a voter chooses to use intermediate ratings. Voter 
education should include the understanding that it is not at all 
obligatory to use these.

Plurality works well, we should understand, when there are only two 
choices. And two-party systems effectively make this the case for 
most voters. The problem is what happens with other candidates, and 
the spoiler effect. Approval and Range deal with this, allowing 
candidates and parties to rise in parity without spoiling elections. 
(An election is "spoiled" under Plurality when the winner would have 
lost in a pairwise contest, but wins because the vote was split among 
opponents, and Plurality provides no way to determine if this is the 
case, because overvotes or ranked votes are not permitted. Range 
technically can also allow a pairwise winner to lose, but only where 
there is another candidate with *broader* support. And that is a 
whole topic of its own, the logic behind Range not satisfying the 
Majority Criterion as usually understood.)

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