Voting with Rubber Bands, Weights, and Strings

Instructions:

This is a 2-split profile. Move the red point to different locations, let go, and see where it settles. Does it always end up at the same point?

Now select the “Mean” button and try it again. Is your answer the same?

▷ Explanation:

All points on the line segment joining the 4 voters minimize the sum of distances to the voters, and all are at equilibrium with respect to the “string-and-weight” forces.

In school, we were taught that the median of the four numbers 1, 8, 9, 11 is the single number 8.5. Is it?

Model:

Mean

Mediancentre

Color Scheme:

Home

Examples:

Π₁ = <0,0,3,0,5,0>
<0,0,2,1,1,1>
2-Split Profile
Smallest M^cBorda Manipulation
Crossing Boundaries
Central Profile
A Stubborn 2-Way Tie
Cross Tie
Irresolute OWM Failure

Figures:

Figure 8 (5-voter descent paths)
Figure 9 (paths for <0,0,2,1,1,1>)
Figure 10 (mean locations, 9 voters)
Figure 11 (mediancentres, 11 voters)
Figure 11B (mediancentres, 15 voters)
Figure 11C (mediancentres, 19 voters)
Figure 11D (mediancentres, 23 voters)

This document is the interactive portion of the paper "Voting with rubber bands, weights, and strings", by Davide Cervone, Ronghua Dai, Daniel Gnoutcheff, Grant Lanterman, Andrew Mackenzie, Ari Morse, Nikhil Srivastava, and William Zwicker, Mathematical Social Sciences 64 (2012) 11–27.