How to vote in Approval

[Joe Weinstein]

Rob LeGrand writes:

"Joe's Rational Strategy and High-Utility Victory-Median Strategy both make 
good sense, but they require estimating each candidate's chances of victory 
from the poll.  What's the best way of doing that?"

Rob then goes on to give an example poll involving candidates C1=Anderson, 
C2=Reagan, C3=Carter, with respective approval percentages being 51, 49, 33; 
  and utilities U1, U2, U3 for you (the voter) being 53, 67, 29.

Well, Rob has asked a good question - how do you estimate each candidate's 
chance of victory?  The answer depends on three sources for variation 
between likely election results (approval percentages) and the poll results. 
  These sources are polling errors, differences in turnout percentage among 
the distinct voting blocs, and changes in bloc size - i.e. shifting of voter 
sentiment - between poll-time and election-time.  (A voting bloc is defined 
by a specific YES-NO stance on each candidate, so here, with three 
candidates, there are eight voting blocs.  Of course, two of these blocs, 
YES-YES-YES and NO-NO-NO, may be disregarded.)  Each variation source in 
turn has two components:  systematic and random.

     Systematic polling error (bias) will in general be undetectable, if 
polling and reporting are done competently:  whatever detectable bias exists 
will be accounted for in arriving at the reported results.  So, if you 
fairly well trust the polltakers and their method, you may as well assume 
zero bias (or else add in a +/- likely bias value into the random polling 
error).

     Random polling error will owe to the above uncertainty in the direction 
of undetected bias, plus finiteness of sample size n:  the smaller n, the 
larger the sample-size-driven random error.

     Systematic differences in bloc turnout percentages may perhaps be 
credibly estimated if blocs can be related to blocs in prior elections.

     Random differences in bloc turnout percentages depend on the blocs' 
absolute sizes: unknown, but well estimated in a good poll from the 
underlying historic plus raw poll data plus known size N of the electorate.  
(In general, the smaller N, the larger the random differences.  A usual 
voting model assumes that prospective voters decide independently on whether 
or not to actually vote (turn out); and that individual voter turn-out 
probability is constant within each bloc.)

     Post-poll shifting in voter sentiment is of course always possible.  
However, this whole exercise - inference from a single snapshot poll - makes 
sense only if we can assume limits to such shifting (on the basis of a 
short-enough poll-to-election time span and the patterns of recent prior 
elections).

When all is done, for the above example we may well get respective victory 
probabilities (percentages) P1, P2, P3 something (crudely) like 60, 40, 0.

     Such a conclusion assumes: random sampling polling error - on the order 
of at most 2% percent per candidate (fairly certain with n=2500, very 
certain with n=5000) - and a smaller limit, 1%, on the effect on each 
candidate's approval percentage of each of the five other above components 
of poll-election variation.

The most important part of this conclusion is that P3=0, i.e. de facto 
chances are nil that C3 will get as many votes as either of C1 or C2.  This 
fact alone will fix your version of the Rational Strategy, with no need for 
precise values for P1 and P2.  Namely, with P3=0 and the fact that for you 
U1<U2, Rational Strategy tells you to vote just for C2.

WARNING - 'STRATEGIC' MINEFIELDS!  Rob's and just about everyone else's 
orthodox discussions - including mine above - of 'strategy' and supposed 
'rationality' - are subject to or based on obvious fallacies.

The orthodox discussions all presume - totally UNREALISTICALLY and thus 
IRRATIONALLY - that voter utilities are based just on who wins (or may win), 
with no regard to the direct costs and benefits of the ACT of voting.

     If the election method allows expressive marking of ballots, the major 
effect of an individual vote is not its putative (but de facto likely nil) 
influence on who wins, but its power of expression of support or nonsupport 
- especially support for hitherto relatively UNappreciated or UNpopular 
candidates or UNvoiced causes  (or nonsupport for hitherto popular 
candidates or causes).

     If this supposedly merely collateral - but in fact usually primary - 
benefit of expression is absent or gagged, it may be quite rational for an 
individual voter to stay home.

For there is a dirty-secret truth about ANY mid-to-large-scale election 
contest (even a 'too-close-to-call' contest such as Florida Pres 2000).  
Namely, in such a contest the de facto probability is NIL that any one 
voter's ballot will matter at all for choosing the winner.

     For this very reason, even an orthodox-mode discussion about 'your' 
'strategy' should make clear EXACTLY WHOSE strategy:  yours as an 
individual, or that of a group which can automatically count on its guidance 
being followed by you and many other voters of a sizeable bloc.

Joe Weinstein
Long Beach CA USA



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