What are we all about?

[Joe Weinstein]

James,

   I never called YOU useless.  I called your apparent (perhaps by me 
misinterpreted) view useless.

Please note that it's quite possible and not dishonorable for an intelligent 
person to hold a view or two that - on deep reflection or in hindsight - 
turns out to be useless.  I would be surprised if at this very moment (and 
most others) I did not hold a number of useless (or, if you like, 
'fruitless') views.

   You write:  ' I'm not aware of anyone interpreting "one person, one vote" 
in this extremely narrow way.  It surely means "one person, one vote, one 
value"? '

Maybe it could or should, depending on what (to you) 'value' means.  Your 
ensuing remark seems (to me) to imply a clarification of this meaning: "But 
this is just where Approval Voting fails, because papers with different 
numbers of candidates marked count for different values in the final tally."

This statement seems to imply that each marked ballot should (at least if we 
unconditionally give priority to the one-person-one-vote principle) 
contribute a fixed (i.e. constant for all marked ballots) sum total amount, 
call it X, to the sum total of all candidates' scores.  This X would rate as 
the 'value' - of the voter's 'vote' or anyhow of his marked ballot.

What is easy to overlook is that in fact Approval can be formulated in terms 
of a scoring procedure which MEETS this criterion.  In fact, YOU may CHOOSE 
the desired X any real value you like.  Then, each ballot contributes 
precisely X points to the tally's total value as follows.  Let N be the 
number of candidates (including allowed number, for any one ballot, of 
write-in candidates), and let A be the number approved (voted 'Yes',=check) 
on that ballot.  The ballot then contributes
P =(X-A)/N points to each non-approved (voted 'No', = blank) candidate, and 
1+P points to each approved candidate, for a sum total of X points 
contributed to the total tally.

This method of tallying an Approval election is fully equivalent to the 
usual Approval tallying method of taking each ballot as contributing 0 
points to each non-approved candidate and 1 point to each approved 
candidate.  The net result of this new method is simply to add to each 
candidate's usual tally the constant VP*, where V is the total number of 
voters and P* is the average value of P over all voters.  The change does 
not affect who wins (or ties), or any two candidates' difference in 
respective scores.

Note that, so long as one takes X at least N, every ballot makes a 
nonnegative contribution to each candidate's total tally.  For instance, 
with three candidates and taking X=5, a ballot which approves two of the 
three candidates is taken to contribute P=(5-2)/3=1 point to the single 
non-approved candidate, and 2 points to each of the two approved candidates.

   You write: 'I cannot determine the value of my vote - the value assigned 
to my vote will be determined relative to the values given to all the other 
votes.'

For the Approval tallying method just noted, this statement does not hold.  
Rather, the 'value' of any marked Approval ballot will be X, the amount 
fixed by design.

Perhaps you have in mind here another notion of 'value', wherein the 'value' 
of a 'vote' (marked ballot) is a kind of measure of the vote's operative or 
instrumental impact.  In this sense, no matter what nontrivial voting method 
be used, 'value' must be quite contingent on other voters' behavior and 
cannot reliably be determined in advance of the tally.  Namely, if 
withdrawal of your marked ballot turns out to make no difference as to 
choice of the winner, then operatively your vote has zero 'value'.  
Otherwise, your vote does have nonzero 'value'.

Inevitably, the possibility - de facto remote - is that some voters may cast 
votes of positive operative 'value'.  Usually, though, in a mass election it 
turns out that all votes are 'wasted', i.e. have zero value, as in the year 
2000 US presidential election - apart from the special aftermath contest 
among the 9 US Supreme Court justices!:-).

   You also write: 'But this is not what we are about.  It is not an 
exercise in "social choice".'

Yes, we are not discussing a mere 'exercise'.  However, I am baffled by (and 
indeed find 'useless' until clarifed) the apparently intended implication 
that choosing a 'representative' is not an instance of "social choice".  As 
one who is not familiar with some academic jargon, I likely miss a 
distinction you are trying to make here between "social choice" 
(deliberately in quotes) and social choice.  As you say, 'it comes back to 
defining the purpose of an election.'

   You also write, apparently about Approval: "the system is flawed [also] 
because my lower preferences count against my higher preferences."

Well, suppose your preferences are (at least in part) A>B>C, A being your 
'best' or 'higher', B being your 'good' or 'lower', and C being your 'bad' 
or 'unacceptable'.  Quite possibly - because of other voters' judgments, 
your 'good' (B) will turn out to be the enemy of your 'best'(A).  That is, 
thanks to the other voters, B will be winner and A in second place.

Approval gives you two OPTIONS.  For one, you may help insure that you get 
an acceptable candidate (A or B) in place of an unacceptable one (C).  
Namely, by voting for both A and B, you can put both your 'upper' and 
'lower' preferences to work against each candidate C that you definitely 
dislike.  This option of course carries the risk that because of your vote - 
AND even more because of where other voters stand - B will thereby just 
manage to defeat A.  If you find the price of this risk too high, then you 
have the opposite OPTION: vote just for A - but then accept that thereby C 
may win office by defeating runner-up B - again, not just or primarily 
because of your vote, but thanks to where other voters stand.

No method, Approval or other, can completely forestall the dilemma that may 
arise from the two legitimate desired objectives:  the best should win and 
the bad should lose.

   With cheers and regards,

Joe Weinstein  (Ph.D.)
Long Beach CA USA






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