[EM] Naive random UWA, timeshare, etc.

[Joe Weinstein]

     Naive random UWA, timeshare, etc.

I didn’t realize that random choice of a single winner is OK with enough 
people on this list, so that it can  be presented without its author getting 
pilloried by determined determinists.  But, now Rob Speer (Messages 11880 et 
seq) has got away with discussing a method, ‘random UWA’,  which uses random 
choice.  So, while we’re at it, here are some personal comments and 
observations and proposals.

PERSONAL COMMENTS.   In the last 15 months I’ve gone from being a determined 
determinist to someone who finds random choice very attractive.

In fact, I no longer believe in mass elections: I think the Athenians, who 
often used random choices to fill offices, had basically the right idea.  
Namely, once given agreed-on objective qualifications for office, randomly 
select from among all willing candidates with those qualifications.  No need 
then for divisive partisan expensive corruption-inducing mass elections.

(And, by the way - subject of a future posting - both individual voter power 
and social utility of an election typically are improved by replacing a 
full-scale mass election by delegation of the decision to a small 
suitably-sized random sample of voters.)

But then, random selection should be my professional tack.  Trained and long 
at work as a mathematician, I am now also an applied statistician.  One 
basic breakthrough in statistical method over the last century was Ronald 
Fisher’s insightful principle of randomization.  That principle may be 
summarized as follows:  once one has spelled out objective qualifications as 
to what sort of individuals one requires or prefers for a given purpose 
(usually, as a ‘representative sample’ of a given population), selection of 
such individuals may as well be RANDOM.  One at least thereby avoids biases 
and favoritism, conscious or unconscious, and moreover gives equal a priori 
selection chance to every qualified individual.

If democracy really means anything, it means that all citizens have a priori 
essentially equal chances of effectively governing - making law and policy.  
Random selection therefore offers a key benefit for those of us who REALLY 
prefer democracy.  (Caution: here in the USA the noun ‘democracy’ and the 
adjective ‘democratic’ are often non-descriptive, even propagandistic: they 
are used to convey the speaker’s approval of whatever devices of government 
are under discussion, even devices which are quite undemocratic.)

By the way, along with random selection, other devices for selection and 
employ of officers can be used to promote democratic participation and to 
frustrate oligarchy and incentives to corruption.  These devices include: 
short terms, with each officer’s responsibility restricted to just one or a 
few decisions; and ad hoc selection (i.e. selection not only random, but 
with little or no lead time).   In short, exactly how we try to pick 
ordinary citizens as trial court jurors.

OBSERVATIONS.  Rob uses pairwise-comparison (alias ‘Condorcet’) ballots to 
define a certain vector of candidate scores - the UWA (‘unique winning 
alliance’).  These scores are weights: they are nonnegative and sum to 1.   
Accordingly, one can choose a winner at random, by using each candidate’s 
weight as his probability of success in the draw.

Note that the SAME ‘random UWA’ approach to selecting the single winner - 
namely, developing a UWA and then using its weights for random selection - 
can be done with ANY balloting and scoring method which gives you a vector 
of nonnegative candidate ‘raw’ scores.

Namely, to get the UWA, normalize the raw scores:  i.e. divide each raw 
score by the total of all raw scores, so that the final scores sum to 1.

Using random UWA with pairwise-comparison seems to me more complicated and 
less natural than using it with some other kinds of balloting and scoring.

In fact, with pairwise comparison, the possible lack of basic monotonicity 
is a real flaw.  (Here,  ‘basic’ monotonicity refers just to cases when a 
voter’s marked ballot’s scores - or preference positions - are changed for 
just one candidate or are interchanged for precisely two candidates.  
Lone-Mark and other commonly discussed  ballot-marking methods exclude or 
greatly constrain more complex ballot changes.)

NAIVE UWA: RANDOM UWA WITH CUMULATION.   There is a very obvious - almost 
NAIVE - choice of method for balloting and scoring which clearly makes 
random UWA selection basic-monotone, and which moreover is fair among 
voters, in that it gives each voter equal and maximum potential impact.  
Namely, any Cumulation method.  In any such method, each voter can allocate 
up to some fixed positive integer number M of points among all candidates, 
and each candidate’s score is simply the sum of all points received from all 
voters.   (The simplest case, M=1, is our pervasive Lone-Mark plurality 
method.)

With Cumulation, the UWA simply registers each candidate’s proportion of 
total support from all voters.  If there are a total of V voters, each voter 
contributes 1/V to the final allocation of probability share in the random 
draw among the candidates.

Random UWA with Cumulation has the signal advantage that each voter’s 
optimal strategies are precisely her ‘most sincere’ ones.  Namely: let her 
allot all M points, in any feasible manner (i.e., so that each candidate 
gets an integer number of points) among all candidates who tie for being her 
top favorites.   Then: there’s NO divergence between sincerity and strategy, 
NO deep secret strategies, and NO advantage to schemers with extra knowledge 
of such strategies.

Used with Lone-Mark plurality or another Cumulation method, Random UWA 
simply takes the vote totals as weights for randomly choosing the winner.  
With this method, no one has to betray any strictly preferred unique 
favorite, or worry about lesser evils.

As claimed for pairwise-comparison, random UWA with Cumulation indeed poses 
no clone problem.  True clones simply share a fixed total UWA weight, no 
matter how their supporters decide to divide votes among them.

TIMESHARE.  Lingering determinists may consult my posting of a few months 
ago, which suggests considering a kind of multi-winner alternative, 
‘timeshare’.  Namely, the candidates take turns in office, with durations in 
proportion to their voted support.  In other words, the UWA weights are not 
for a single random draw but for allocation of time in office.

As I pointed out, some days (or hours) in office may be deemed worth more 
than others.  Hence, some kind of randomization procedure may be useful to 
specify the order whereby the candidates fill the office.

Joe Weinstein
Long Beach CA USA

_________________________________________________________________
Tired of spam? Get advanced junk mail protection with MSN 8. 
http://join.msn.com/?page=features/junkmail