[EM] A modified Random Ballot that supports compromising

[Jobst Heitzig]

Dear Forest,

You wrote:
> Martin suggested listing all of the candidates in order of approval
> count, and then on each ballot circle the candidate approved on that
> ballot that is highest on the list.  Each ballot has one candidate
> circled, so each voter ends up supporting exactly one candidate.

That's very similar indeed and even simpler.

> Do a plurality count of circled candidates.  It's not hard to show
> that the Plurality winner is always the highest candidate on the
> list, i.e. the Approval winner.

So his was not a new method but a new interpretation of Approval Voting?

> Your method is an improvement in some ways, but how to eliminate
> dangerous candidates w/o destroying the nice properties???

First, why don't I just circle the most approved candidate on each
ballot? Because I want to ensure that each group of p% of the voters can
distribute their share of p% of the probability independently from the
other voters, as in Random Ballot, but with an easy way to cooperate and
support compromise candidates without having to order reverse.

Second, how can we make sure no dangerous candidate can be elected? My
conjecture is that in any system that does not give a mere majority 100%
of the power, dangerous candidates can only be avoided when they are
considered dangerous by a very broad share of the voters, say 2/3. The
easiest mechanism would be to simply let voters mark candidates they
consider really dangerous with a minus sign and exclude all who receive
more than 75% minus signs. In the very unlikely event that no candidate
remains, the election should be repeated, thereby disencouraging misuse
of the minus sign somewhat. So my suggested method is this:


75%-SAFEGUARDED APPROVAL-PRIORITIZED RANDOM BALLOT (SAPRB75)
------------------------------------------------------------
1. Approval style ballots with the option of striking out candidates
which one considers really dangerous for society (not just unwanted).
2. Eliminate all candidates stricken out by more than 75% of the voters.
If no-one remains, repeat the election.
3. Determine the approval winner among the remaining candidates, using
all ballots (in the first iteration of this step) or only the remaining
ballots (in later iterations of this step). On all of these ballots
which approve this candidate, mark this candidate and put these ballots
aside.
4. Repeat step 3 as long as there are some remaining ballots.
5. From all ballots, draw one at random. The winner is the candidate
marked on that ballot.


This method is still monotonic and cloneproof and gives the largest
probability to the most approval candidate not considered dangerous by
75% of society. Only very large majorities can oppress the rest of
society by using the safeguarding option strategically.

Jobst