[EM] Directional Resistance

Forest W Simmons fsimmons at pcc.edu
Thu Mar 22 12:53:45 PDT 2007

Michael Poole worried that it might be impossible to find circuit 
elements with the precise properties needed.

As always, theoretical circuits have elements with idealized 
properties.  An idealized diode of the kind we need with reisitance R1 
in  one direction and R2 in the other direction could be constructed 
out of some combination of linear resistors and perfectly rectifying 

Suppose that R2 is the larger resistance.  Then put a linear resistor 
of resistance  R3=R1*R2/(R2-R1) in series with a perfectly rectifying 
diode, and put the resulting compound circuit element in parallel with 
a linear resistor of resistance R2.

His other question was what does resistance have to do with elections.

short answer:  voters who rank candidate i over candidate j are 
manifesting resistance to the election of j, at least in comparison 
with candidate i.

Jobst correctly divined that the method is not clone free.  Here's an 


The idealized diode resistances are

R(A,B)=2, R(B,A)=3, R(A,C)=2, R(C,A)=3, R(B,C)=0, R(C,B)=5

The respective circuit resistances are

r(A,B)= 1/(1/2+1/7)=14/9=1.5555...
r(B,A)= 1/(1/3+1/3)=3/2 = 1.5
r(A,C)= 1/(1/2+1/2)= 1
r(C,A)= 1/(1/3+1/8)=24/11=2.181818...

The min max circuit resistance of 1.5 ohms is that encountered by B 
when the DC current flows from B to A.

>From A to B the circuit resistance is slightly larger: 1.555... ohms.

The max circuit resistance to C is 2.5 ohms.

So B is the winner.  But removing B's clone C makes A the winner, as 
you can easily check.

Note that the teaming effect is not quite as bad as Borda's, since here 
B just barely wins, whereas in Borda B has a nice margin of safety.

Could this method be better than Borda for calculating tournament 
winners in Round Robin sports contests?

Perhaps the Electrical Engineers could adopt it if they decide to have 
a volleyball team playoff.


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