Voting with Rubber Bands, Weights, and Strings

Instructions:

Click the red point to start the simulation and observe where the point comes to rest.

Change to “Mean” and try it again.

Now go back to “Mediancentre” and press the <0,3,3,0,1,1> button below to view another profile that also produces a tie between these same rankings. Finally, press the <5,5,8,2,1,1> button to see the sum of these two ties.

Note that adding the two ties does not result in another tie!

▷ Explanation:

The initial profile here is an example of a cross tie. Such configurations represent the only examples we have found of M^cBorda ties that are not also Borda ties, and require an even number of voters.

The second profile exemplifies a bilateral tie. It is easy to see that anonymity + neutrality force ties for these configurations. In particular both M^cBorda and Borda yield a two-way tie between p and r for this example.

It may seem strange that when we add two profiles, each of which individually yield a M^cBorda tie between p and r, the result is a profile in which r is the sole M^cBorda winner. This represents a failure of the consistency axiom.

Model:

Mean

Mediancentre

Color Scheme:

Home

Examples:

Figures:

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.