[EM] Why use more than two grades?

[Bart Ingles]

Joe Weinstein wrote:
>
> In response (1/17) to my last posting (1/16), Bart Ingles asks:
> 
> > "One question: why would any voter want to vote anything other than 0.0 or
> > 1.0 for any individual candidate?  I understand that a voter may be truly
> > undecided about a candidate, but in that case why wouldn't a coin-toss serve
> > just as well?"
> 
> WHY ME? To be fair, these basic queries ought to be put not just to me but
> to ALL advocates of what are in effect higher-resolution grading methods
> (more than two grade values allowed).     [...]

The question was intended for anyone who cared to answer -- the 'you'
was meant in the colloquial sense.  I certainly didn't intend a personal
attack or insult.

And don't think you are the first person to have considered a graduated
voting system.  I would venture that most of us have done so, before
settling on what each of us considers to be the ideal system.  I started
out advocating Instant Runoff, and then went through a phase of
exhausting various ratings-based methods, before concluding that they
don't really add anything substantive to the election process.

One reason I discount both cardinal and ordinal systems, at least for
use in single-winner elections, is that unlimited choices don't really
give the voter more power on balance, even with some theoretical
'perfect' system.  The reason is that while you can make more
distinctions, so can all of the other voters.  Some of these
distinctions will be strongly held and some will be trivial.  Another
voter's trivial choices can thus cancel out your strongly-held ones. 
The ensuing opinion-clutter might then choose an almost random winner.

By restricting the number of choices each voter can make, you encourage
each voter to make the most of the available options and to vote based
on his/her most important criteria.  The outcome is thus more likely to
satisfy the most important requirements for the largest number of voters
-- i.e. a consensus.

You might argue that allowing cardinal vs. ordinal numbers would allow
voters to give smaller numbers to trivial distinctions, but this is just
a matter of degree (another voters trivial 0.2 vote might only cancel
20% of your 1.0 priority vote).


> RESPONSE TO FIRST QUERY. For many intimate or smaller-scale elections,
> pass-fail (‘approval') grading, using just two grades,  will be adequate -
> and may be required for simplicity of tabulation.  However, in larger or
> more public elections, with thousands or even millions of voters, use of
> higher-resolution grading will impose little or no extra burden on the
> already requisite computerized tabulation.  Moreover, as it is unlikely that
> any outcome will be determined by a single vote, a major electoral function
> and voter motivation - and arguably a civil right of both voters and
> candidate - is conferred when the available grade levels allow a voter V to
> express her (or his) evaluations to higher resolution.

It all depends on the degree of resolution you want to allow, I
suppose.  Approval voting requires only one optical bubble or punch card
position per candidate.  For graduated voting, you would require (N -
1)  bubbles per candidate, where N is the number of levels allowed.  So
for three levels, the graduated ballot would have to be twice as long as
an Approval ballot.  In theory you could reduce ballot size binary
encoding or some such, but in practice I don't think this would get very
far.

Of course grading would be easier with some sort of touch-screen or
computer terminal balloting, but I don't believe there would be enough
benefit to justify the cost if such a system is not already in use.  And
if I'm going to put energy into advocating an improved voting system, I
would prefer it to be one which could be used anywhere and not just in
well-to-do counties (or countries).


> In brief, a voter V should (and may as well, given modern technology) be
> enabled to better express her grade of each candidate.  Closer realization
> of this goal is a major reason for considering alternative election methods
> at all.
> 
> Even with just two candidates, V may well wish to ‘send a message' to future
> politics, that her favored candidate has most, but far from all, of her
> support.  For example, she may wish to vote A 0.6, B 0.0 . Or, with three
> candidates, she may wish to express a judgment that B is much  worse (or
> anyhow much less worthy of support) than A but much better than C, e.g.: A
> 1.0, B 0.6, C 0.1.   For a 6 Nov. 2000 example using candidates initials
> (with IW =Ideal Write-In), I myself wanted to vote something like: IW 1.0,
> AG 0.8, RN 0.7, HB 0.3, GB 0.2, PB 0.0.

I think that self-expression is an important side-benefit of voting,
especially for those whose favorite doesn't stand a chance of winning,
but the primary purpose of elections must be to elect the most suitable
candidate based on the votes.  Besides, there are more effective ways of
expressing your views in ways that others will see. 


> Maybe most voters in most elections will not care to use the grading option
> to its fullest degree.  That situation would contradict neither this
> option's benefits nor its very necessity, as a attainable civil right of
> free expression, for voters and candidates.  One could as well rule out any
> one of some better-known civil rights and liberties, e.g. freedom of speech
> or of the press, on the grounds that relatively few citizens ever use these
> options to their fullest, or at all.

I'm not sure what 'using the grading option to its fullest degree' means
-- if the intent is to affect the outcome, then it means voting the
maximum or minimum for each candidate under Cardinal Approval Voting,
and giving all fractional votes to one candidate under Cardinal
Cumulative Voting.

Any other arithmetic-based system, such as the one based on
hyperspheres, would probably have strategies similar to Cumulative
Voting, since giving some of your vote to a second candidate still
reduces your vote for your favorite (or your strategic choice), albeit
to a lesser degree.  In other words, such a system would be equivalent
to single-vote plurality.


> RESPONSE TO SECOND QUERY.  If voter V truly cannot credibly assign candidate
> C some minimal nonzero grade, then C may as well receive the grade 0, -
> either explicitly from V, or by automatic default from V's failure to mark
> any grade for C.

That was actually a serious question.  If you really want to give a 0.5
vote to candidate C, you can simulate this by tossing a coin and giving
the candidate 0.0 or 1.0 based on the outcome of the toss.  If other
voters do likewise, the candidate should get 0.5 on average from each
candidate (if other voters aren't similarly undecided, it won't matter
much).  For finer resolution, you can use a pair of dice from a Monopoly
game.

Another option would be to get together with a like-minded voter, and
mark up your absentee ballots so that one contains a vote for C and one
doesn't.

Bart