[EM] Sincere voting

[Joe Weinstein]

Many recent EM-list postings unwittingly illustrate how hard it is to define 
- let alone fruitfully exploit - the notion of a given vote (voter's ballot 
marking) being ‘sincere'.  ‘Sincerity' per se seems a fruitless quest, but 
our interest in the concept does reflect our key concern - election methods 
which allow voters' desires to be more readily expressed and realized.  The 
following comments examine just how and why ‘sincerity' is so problematic - 
in general and in voting.
Joe Weinstein
Long Beach CA USA

‘SINCERITY' IN GENERAL.  Here's a working general definition.  A person's 
utterance - or a similar expressive action, e.g. a vote (marking of a 
ballot) - is ‘sincere'  (and the person is ‘sincere', at least in making the 
utterance or in casting the vote) if the beliefs or attitudes conveyed by 
the utterance are in accord with the person's body of relevant beliefs (or 
attitudes).

Various disagreements found in recent EM-list postings owe to the 
significant INHERENT ambiguities in the above (or similar) notion of 
sincerity.  These arise at least from the following ambiguities in the above 
key terms ‘conveyed', ‘accord', and ‘relevant'.

	‘Conveyed'.  Beliefs (or attitudes) are covert and private, whereas 
utterances are overt and public.  In effect, a belief is an expression 
within a rich covert language, which may or may not readily translate 
exactly - or even to what may be deemed good-enough approximation - into the 
overt language used in an utterance.  Just which relevant beliefs are thus 
‘conveyed' by the utterance?  Presence of ‘sincerity' must depend on the 
answer taken to this question.

	‘Accord'.  As the term ‘accord' indicates, sincerity requires that a 
certain logical relationship exist between the relevant beliefs conveyed by 
the utterance and the totality of the utterer's relevant beliefs.  Exactly 
what is this relationship?  A MINIMAL concept of ‘accord' requires only that 
the utterance NOT CONTRADICT utterer's relevant beliefs.  A MAXIMAL concept 
requires that the utterance AFFIRM ALL these beliefs (i.e., not only be ‘a 
truth' but ‘the whole truth', which usually is a practical impossibility).  
Intermediate (usually vaguer) requirements are that the utterance must 
affirm a sufficiently salient part of these beliefs.

	‘Relevant'.  Presence of ‘sincerity' typically depends not on all beliefs 
but just on ‘relevant' ones.   Relevance may depend highly on the context.  
For instance, when your hearer is anxiously awaiting your declaration of 
love (or possibly of rejection), you may be judged highly insincere if you 
exclaim ‘2+2=4', even though you do truly and even intensely believe that 
2+2=4.

	Each of these three terms is actually triply ambiguous, because it leaves 
open just who - ourselves, the utterer, or the listener - is to be the judge 
that resolves the term's ambiguity.

VOTING EXAMPLE.  Suppose that your attitudes include evaluations for four 
candidates, A-D, using ratings (on a scale of 0.00 to 1.00):   A=0.75, 
B=0.75, C=0.45, D= 0.00.  Now suppose that you vote: you mark the ballot by 
giving each candidate an integer grade (zero or higher).

	The prevalent lone-mark (i.e. ‘plurality') method allows just one nonzero 
grade, namely a 1 (‘pass').  Suppose your lone pass is for A.  Does your 
vote qualify as ‘sincere' or not?  In one sense, it is as sincere as the 
method allows it to be; in another sense, it is quite insincere (albeit such 
insincerity is forced by the method) as it does not at all come close to 
expressing what you or maybe others deem important aspects of my evaluation: 
that A and B are rated equally, and that B and C are each far closer to A 
than to D.

	Now suppose you revote under the pass-fail (i.e. ‘approval') method, which 
allows any set of pass (=1) and fail(=0) grades.  Suppose your vote is: A=1, 
B=1, C=1, D=0.  Is this vote ‘sincere'?  In one sense, it is as sincere as 
the method allows it to be.  Namely, candidates evaluated above some 
threshold (e.g. 0.40) get passed, while the others get failed.  Moreover, 
this particular vote gives as large as possible gap between the lowest-rated 
passed candidate and the highest-rated failed candidate.  However, in 
another sense the vote is quite insincere (and this time not because the 
method forces it to be), as it gives to B the grade 1 rather than 0, 
although B's rating is closer to 0 than to 1.   Another insincerity (which 
also holds with lone-mark) is forced by the fact that only two grades are 
available, so that your vote cannot express the fact that your degrees of 
preference for A over C and for C over D are both significant.

	Now revote under a strict-only ranking method, e.g. iterated reduction 
(‘instant runoff') or usual Borda.  Suppose your vote is: A=3, B=2, C=1, 
D=0.  (A is top choice, etc.)  Much the same arguments for sincerity and 
insincerity apply as were cited above for lone-mark (‘plurality').

The above-cited contradictory informal judgments of sincerity and 
insincerity all reflect various opinionated but plausible choices which 
could be made by a minimalist (on the issue of accord) to resolve the 
above-noted ambiguities of conveyance.   (Meanwhile, for a maximalist, 
typically no vote at all can qualify as sincere.)  For some minimalists in 
some cases, vote truncation (so that, for example, only candidate A receives 
a grade) might change their view of the vote from insincere to sincere, as 
the vote would contain fewer specifications which might be deemed to 
contradict significant features of the set of ratings.

Among other things, we see that - under usual resolutions of ambiguities of 
conveyance and accord - each of the above-discussed methods often (i.e., for 
many sets of ratings, as in the above example) permits no sincere vote 
whatever.

The underlying reason is quite simple: none of the methods always allows 
grades which simply and directly express your ratings, but rather each 
method imposes constraints on the allowed grades.  (For the case of 
pass-fail, the constraint arises from the low resolution of the grading, 
i.e. just two grades are available.  Each other method has, instead or in 
addition, a trade-off constraint: a higher grade for one candidate requires 
a lower grade for some other candidate.)

In order to avoid being embarrassed when no sincere vote is possible for you 
under my favorite method, I might try to exploit the third ambiguity source: 
relevance.  Now, few people overtly deny the relevance of ratings of 
candidates, at least in principle.  In fact, even if one presumes that, in 
voting, only ‘political' beliefs and attitudes are relevant, it is hard to 
discern any precise limits for such relevance. However, I could try to claim 
that certain features of these ratings (namely the features whose expression 
your method hinders or forbids) are irrelevant ‘strategically', i.e. for 
practical purposes of voting. Thus, as a pass-fail partisan I could claim 
irrelevance of an intermediate grade between full pass and full fail; or, as 
a partisan of strict-only ranking, I could claim irrelevance of equal grades 
(e.g., the case of a first-place tie).  A followon posting will consider 
such claims.

DEGREE OF SINCERITY.  The notion of ‘sincerity' is not only absolute, but 
relative, a matter of degree.  As in the above examples, full or absolute 
sincerity may at times be disallowed by the election method, but anyhow some 
votes do seem ‘more sincere' than do others.  Enabling ‘more sincere' voting 
is certainly a major goal in our quest for better election methods.

Degree of sincerity can be quantified when, as above, one of the above-cited 
election methods is used and moreover each voter's relevant beliefs are 
taken to be expressible via a set of ratings. Using a suitable index of 
distance or discrepancy, a vote's insincerity can be equated  to the 
calculated discrepancy between the actual vote and the nearest fully sincere 
vote. (Actually casting the latter may well be disallowed by the election 
method.) Mathematically there are various ways to define such an index.  At 
this point, preference for one index over another seems largely a subjective 
matter.

SINCERE VOTE V. SINCERE EFFECT.  All the above is just the start of the 
‘sincerity' capers!  For example, it is quite possible that a method allows 
sincere VOTING but ensures insincere (or anyhow not fully sincere) SCORING 
of the candidates.  That is, at times there will be no change in scores if 
some one voter's sincere vote be replaced by an insincere vote.  Such is 
exactly what happens in US presidential elections: change of a single vote 
will in general not change the candidates' scores - namely their electoral 
vote counts - which are used to decide the winner.

Election methods featured in this list's discussions suggest other 
possibilities for deriving such insincere-scoring methods.  In particular, 
suppose that (as above) the relevant beliefs are taken to be fully expressed 
via the voters' grade-ratings of the candidates, and that (as usual) a 
candidate's score is got by summing his or her grades.  To get a 
sincere-voting-insincere-scoring method, just take each summed grade to be 
not the actually marked ‘raw' grade but a suitably transformed value.

For instance, transform each raw grade to 1 (pass) or 0 (fail) according as 
the grade is at least c or not, where c is a desired criterion value 
(between 0 and 1), say c=0.50.  Or, transform each ballot's set of raw 
grades to ranks.

THANKS FOR YOUR HEED.  -  Joe
_____________________________________________________________________________________
Get more from the Web.  FREE MSN Explorer download : http://explorer.msn.com