[EM] Welcome! / Procedural version of DFC

[Jobst Heitzig]

Dear Abd ulRahman!

Welcome to the list from me, too.

What do you think about the following story (leading to a group decision
method somewhat similar to DMC):

Consider a group of people having to decide for one out of a number of
options.
   At first, they may think that deciding by a "simple vote" would be
both easy and efficient. So they come together and let each one raise
her hand for her favourite option.
   After a number of these "first past the post"-decisions they realize
some problems. Sometimes some individuals have not enough information to
decide for a single favourite or are undecided for other reasons, so the
group changes the system and allows for abstention. But they realize
also that sometimes two very similar options both lose but would have
won if only one of the two would have been suggested (the "spoiler"
effect). And they realize that moderate compromise options often lose
because the group tends to be polarized between two extremes one of
which will win instead of the compromise. Finally, there may be rare
occasions where some member of the group tries to "cheat" and vote for a
second option as soon as he realizes that his favourite has no chance of
winning.
   For all of these reasons someone suggests that they simplify the
voting procedure slightly by letting everyone vote for as few or as many
options as they like. Although some object that this would violate "one
man one vote" and would therefore give some voters more power, they give
it a try and soon find out that it's not true that the more options you
vote for the more weight your vote has. So they switch to the new
system, and at first it seems to work much better and avoid the problems
they had.
   But after a number of these "approval voting"-decision they realize a
strange effect: sometimes only few voters actually make use of the
possibility and most still only vote for one option, although often it
is clear that they in reality also approve of another option. After some
analysis they find out that this insincere "bullet voting" has various
strategic reasons. Someone suggests to get back to the old system, but
upon closer inspection they find also evidence of strategic voting in
the old system.
   Now someone makes a somewhat "unorthodox" suggestion: In order to
avoid choosing a bad option only because of strategic voting, they treat
the first voting round only as a kind of poll to base the real decision
upon. The real decision would go like this: one of the group is declared
the "moderator" by lot. The moderator's duty is to pick what seems to be
the best compromise option in view of the information from the first
round. If s/he picks the option with the most votes, that options is
indeed declared the winner. But if she picks a different option, this
choice is then checked by the group like this: because each option which
got more votes than the moderator's option seems to be a better choice
at first glance, the moderator asks the group to affirm by simple
majority vote that her picked option is actually a better compromise
than the other option. If the picked option wins all these pairwise
comparisons, it is declared the winner, otherwise the moderator must
pick a new option until a winner is found.
   Although this seems to be more complicated than the other two
systems, and even introduces some randomness because the moderator is
chosen by lot, over the time they find a number of advantages of the
third system: First of all, it is much harder to mess up the result by
voting strategically, because of the additional check and because that
check is lead by a randomly chosen person. Second of all, it turns out
that sometimes there is an option which beats all others in direct
pairwise contests but would not have won in either of the first two
systems; whereas the new system gives such "Beats-all-winners" a fair
chance of winning because the moderator need only pick this option and
it will win. Also, minorities will not so easily get the impression of
being oppressed by a majority since they still often have the chance to
improve the result by providing the moderator. The chance to become the
moderator also encourages thinking about compromises instead of only
thinking of one's favourite, and this can finally lead to suggesting
getter compromises in the first place. Finally, the additional "check"
gives everyone the feeling that the system is safer and uses more of the
available information than the other two; obviously wrong decisions are
much less probable.


Now, although I used many words to introduce this group decision method
to you, I still think it is very easy to understand the procedure and
the reasons for it, do you agree?

Yours,
Jobst


PS: The above method makes use of Forest Simmons' idea to combine
pairwise preference defeats and approval defeats. I call it "Democratic
Fair Choice" (DFC). The set of possible winners (= those options which
would win if the moderator picks them = those options which beat all
more-approved ones in pairwise comparisons) always includes the Approval
winner, the DMC winner, and the Condorcet winner, if one exists. The
random component can be interpreted as using the well-known method
"Random Ballot" to choose from a set of "good" options. Hence the method
can be considered a compromise between three classical approaches,
namely Random Ballot (good because of perfect strategy proofness),
Approval Voting (good because of simplicity and efficiency when voters
are honest), and Condorcet (gives great stability against
a-posteriori-complaints). A version of DFC designed for public elections
is in the wiki:
http://wiki.electorama.com/wiki/Imagine_Democratic_Fair_Choice