<br><br><div class="gmail_quote">2012/2/3 David L Wetzell <span dir="ltr"><<a href="mailto:wetzelld@gmail.com">wetzelld@gmail.com</a>></span><br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
What if the electoral space goes back and forth between a 2-d space and a 1-d space?<div>For every election, there's a randomly generated weight given to the 2-ds that has some continuity over time. </div><div>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. </div>
<div><br></div><div>Now, let's postulate a <a href="https://www.google.com/search?aq=0&oq=cob-web+model&sourceid=chrome&ie=UTF-8&q=cobweb+model" target="_blank">cob-web model of decision-making. </a></div>
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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.</div><div> </div></div><div>OTOH, a new party's candidates enter into 2-d space anywhere based on the new period's weights. </div>
<div>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. </div><div><br></div><div>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...</div>
<div><br></div><div>[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.... ] </div>
<div><br></div><div>More importantly, we need some sort of "money" on the table to justify entrance and exit, movement and maybe the merger of parties. </div><div>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+.]</div>
<div><br></div><div>Finally, we'd need to come up with a way to measure and assess the outcomes.</div><div>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. </div>
<div>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. </div>
<div><br></div><div>I think IRV+ will perform well in the mixture assessment. </div></blockquote><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><br></div><div>
Any thoughts/suggestions?</div></blockquote><div><br></div><div>1. I disagree; I do not think IRV will do well in the scenario you describe.</div><div><br></div><div>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.</div>
<div><br></div><div>jq </div></div>