Dear Warren and list members,
you wrote:
The main differences, however, are these:
- Voting money is transferred on a regular basis, not only in the very rare
case of swing voters, thus making the strategic incentive much stronger.
--this is good. However, in one of your revised schemes you
made the "deciders" become a very small fraction of the population
instead of (as originally) 1/3.
That means very few voters are connected to reality via
(your equivalent of) Clarke taxes.
I think you have a DILEMMA:
A* If you make there be many deciders, then the compensators
tend to pay too much money.
B* If you make there be too few deciders, then a voter
is unlikely to be a decider, and hence her economic incentives
to vote honestly, are diminished.
B was also a problem with CTT voting - the Clarke payments were rare,
divorcing voters from reality.
Need to seek the best tradeoff between A & B.
That could be another reason for using the averaging process of version
2, since it treats all voters alike as potential deciders, so it
distributes the incentive evenly.
- The transfers are so designed that they compensate those deciding voters
who get a worse result than with the random ballot lottery, thus keeping
with the philosophy that that lottery is to be considered the benchmark for
every more efficient choice.
--the random ballot lottery (unfortunately?) is a pretty low benchmark.
Low only in terms of efficiency. But the focus is not on efficiency here
(that is solved by electing the option maximizing the average rating)
but on equality and fairness. In my opinion, every voters has a priori a
right to distribute a share of 1/N of the winning probability. So if a
method takes away this control, it has to compensate the voter. (You
might remember that we had this "benchmark" discussion already about a
year ago... :-)
You could also consider the "random candidate lottery"
(elect each with probability 1/K, where K candidates in all).
That is an even-worse benchmark than random ballot, but it is simpler
and does not depend on the votes at all. Because it does not depend
on votes, you then would not need your "benchmarker" class of voters,
only deciders and compensators.
See above for the motivation why it is exactly the Random Ballot process
which has to serve as the benchmark in my view. Also, a random candidate
lottery is not clone-proof.
- Voting money is not destroyed and then gradually refilled but is always
preserved, thus keeping its value constant.
--Is there a worry that over a sequence of elections, we get unfairness?
That might occurr if the variance of the adjustments is too large, so
that it could happen that only by sheer bad luck a voter's account
becomes negative and the voters cannot influence the next decision until
her account is positive again. Also for this reason the variance of the
adjustments due to the random assignment of groups should be as small
as possible.
In election #1, suppose you are correct and so everybody
wants to vote honestly. Excellent.
BUT now in election #2, some voters have more "money" than others,
hence have more power. COULD IT HAPPEN THAT this
inequality could be CORRELATED with the politics?
If so, then in election #2, the "Democrats" would win, unfairly, purely
because Democrats have more power. If this could somehow
feed back (so that in election #3, democrats also tended to have more
money, and so on forever) this could be extremely bad.
Hmm... I hope the feedback will always be negative, partly because the
benchmark against which compensations are determined is not the majority
choice but the "average" choice (Random Ballot).
Also, your benchmarkers could have motivation to vote DIShonestly,
thus defeating the purpose.
CONCRETE SCENARIO TO WORRY ABOUT:
The benchmarker votes affect the payouts. If benchmarkers
dishonestly rank the Democrat top, that tends to cause those who
rate Democrats low, to get lower payoffs. That causes
Democrats to have more money in election #2. That causes
this strategy to work even better in election #2. Feedback.
Disaster.
(I'm not sure whether this scenario is a real problem. But it might be.)
A REPAIR:
Note that in the random-candidate-lottery there are no benchmarkers,
hence the worry I just described perhaps no longer exists.
-wds
Let us think about this some further. My hope is that because (i) a
voter does not know whether she is a benchmark voter, and (ii) the
benchmark group will usually be a representative sample of the
electorate, and (iii) the averaging process of version 2 treats all
voters alike when it comes to adjustments, the incentive described by
you will be averaged out if it exists in the first place. But surely
this deserves more detailed research...
Yours, Jobst
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