[EM] A four bit (sixteen slot) range style ballot

[fsimmons at pcc.edu]

Here's the use I had in mind for the four bit ballot:

0. For each four bit ballot create four pairwise matrices, M1 based on the most significant bit, M2 based 
on the first two significant bits, M3 based on the first three significant bits, and M4 based on all four 
significant bits.

1. The matrix M1 will automatically have a  beats all alternative, namely, the alternative A with the 
greatest number of ballots on which the first bit was marked.  Use this alternative A to initialize a variable 
X.

2. While the current value of X is uncovered according to M2, replace X with the alternative that M2 
covers this value of X with a new value of X against which the current value gives the least M2 pairwise 
oppostition.

3. While the current value of X is uncovered according to M3, replace X with the alternative that M3 
covers this value of X with a new value of X against which the current value gives the least M3 pairwise 
oppostition.

4. While the current value of X is uncovered according to M4, replace X with the alternative that M4 
covers this value of X with a new value of X against which the current value gives the least M4 pairwise 
oppostition.

5. Elect the final value of X.

Note that at the end of steps 1, 2, 3, and 4, respectively, the value of X is uncovered according to 
matrices M1, M2, M3, and M4, respectively.  Each numbered step refines the previous result.

The reason that I suggest using the covering alternative against which the current champ offers the least 
pairwise opposition is to minimize the incentive for insincere strategy:

If X2 covers X1, and among all of the candidates that cover X1 is the one against which X1 offers the 
least pairwise resistance, then X2 is the natural compromise candidate for X1 supporters.  

Furthermore, X1 supporters do not have to rate X2 above X1 to increase X2's chances of being the one to 
replace X1.

Comments?

Thanks,

Forest