Mathematical analysis MD PART 1
Let us say there are N+1
voters with X possible rankings. Let us say you arrange all the
voters in the positions XA – (i) where XA – 0 is the lowest number value assigned to
candidate A and XA – 4 is the greatest. The median voter for candidate A will be XA(i)
where (i) = (N/2) we will call the median vote value
Φ
(Nota bene if the number of voters
is even there are when proceeds in the same fashion except one take the average between
XA(i) where (i) = (N/2)and
XA(i) where (i) = ((N/2) +1) i.e. for 6 voters with positions
btw 05 one averages 2 and 3
If there are several votes of the same value simply proceed normally and give each an
independent position.)
I
MD Mathematical part 2 = NFLUENCING
There are N/2 voters who vote below
Φ
and N/2 candidate who vote above
Φ
.
If I am an individual voter I can influence the election one of three ways
1)
he is the
median voter
he is between then any number he select $ will be the median so long as
XA((N/2)1)
< =
$ <= XA((N/2)1)
he whatever he changes his vote to will be the
median.
2) SHe votes for a number $ that is < XA((N/2)1)
then XA((N/2)1)
becomes the new median which is by definition <= the previous median.
3) SHe votes
for a number $ that is > XA((N/2)+1)
then XA((N/2)+1)
becomes the new median
which is by definition >= the previous median.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '11
 stevenjbrams
 Candidate, Voting system, xa, Plurality voting system

Click to edit the document details