[EM] Directional Resistance

Jobst Heitzig heitzig-j at web.de
Thu Mar 22 02:44:33 PDT 2007

Dear Forest,

nice idea, but I'm almost sure it will not be cloneproof. Consider three 
options x,y,z. Then the circuit resistance from x to z is 
  1 / (1/Rxz + 1/(Rxy+Ryz)).
When we add a y-clone y', it seems we get
  1 / (1/Rxz + 1/(Rxy+Ryz) + 1/(Rxy'+Ry'z))
which is smaller. Although all other pairwise circuit resistances will 
also decrease, it seems that this will not happen in such a coordinated 
way that the winner is preserved. 

Yours, Jobst

> Has anybody explored this idea?
> Make an electrical circuit with a terminal for each candidate.
> For each pair of terminals attach a diode that has a different
> resistance in each direction: the resistance in the direction from
> candidate i to candidate j is proportional to the number of ballots
> on which candidate j is ranked above candidate i.
> After all of the diodes are attached measure the circuit resistance
> between terminals i and j.
> The candidate X against whom the maximal resistance is minimal is the
> winner.
> Forest
> ----
> election-methods mailing list - see http://electorama.com/em for list
> info
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