[EM] brainstorm'n electoral calculus on acid...

[David L Wetzell]

What if the electoral space goes back and forth between a 2-d space and a
1-d space?
For every election, there's a randomly generated weight given to the 2-ds
that has some continuity over time.
Like lets say that the weight given to one dimension at time t is vt and
the weight to the other is 1-vt and vt is based on an xt variable that goes
from negative infinity to positive infinity such that
vt=Exp(xt)/(1+Exp(xt)) and xt= .8*xt-1 + ut and ut has a standard normal
distribution.

Now, let's postulate a cob-web model of decision-making.
<https://www.google.com/search?aq=0&oq=cob-web+model&sourceid=chrome&ie=UTF-8&q=cobweb+model>

Existing party's candidates make decisions in 2-d space, using vt-1 weights
and some sort of friction that inhibits their ability to reposition within
each of the two dimensions.

OTOH, a new party's candidates enter into 2-d space anywhere based on the
new period's weights.
However, the new party makes its entrance decision based on a cost-benefit
decision using the incorrect assumption that voters make decisions based on
the 1-d of this period.

However, voters actually decide based on the weighted average of this
period and last periods' 1-d positions of candidates relative to them.
 Let's just use a 2-period moving average for now.  They treat the prior
period distance of the new party's candidate as the closest corner on the
1-d space...

[There also needs to be some expected utility and fixed disutility from
voting that determines who votes and who does not vote to enable the de
facto center to be severed from the true center but that feature could be
introduced later.... ]

More importantly, we need some sort of "money" on the table to justify
entrance and exit, movement and maybe the merger of parties.
If I had to choose between endogenous voter-participation and endogenous
party participation, the latter would be more relevant, since we're talking
about the desirability of a 2-party vs multi-party system and the no. of
parties really needs to be endogenous.  So how do we keep the "losers" in
the game?  Obviously, there's going to be a certain taste for political
participation that is based on the strength of their support which lets
them absorb some losses.  [Another twist would be to also have a less
valuable 3-seat election, using LR Hare, that would give two or three
parties some additional cash-flow... and which could try out my IRV+ + Am
forms of PR idea, with other election rules replacing IRV+.]

Finally, we'd need to come up with a way to measure and assess the outcomes.
Here we need a weighted average of the diff between the winner and the true
center in 1d and the lack of variability of the winner in 2d.
This allows that nailing the center, or electing the CW, is not the
end-all-be-all for how to assess election rules.  We could compare and
contrast the relative performance of election rules in three cases.  The
first would be where all the weight is on the distance from the true
center.  The second would be where all of the weight is on the stability of
the winner in 2 d.  The third would be a mixture of the two, perhaps to be
progressive 2/3rds on getting closer to the center and 1/3rd on the lack of
variability.

I think IRV+ will perform well in the mixture assessment.

Any thoughts/suggestions?

dlw
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