2012/2/3 David L Wetzell <[email protected]> > 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? > 1. I disagree; I do not think IRV will do well in the scenario you describe. 2. It's too complex. We need toy models that focus on one aspect at a time, not anything that tries to be realistic. Think macroeconomics 101 (saltwater), where anything that doesn't fit on one graph is put off until next year. jq
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