11A          Does the Majority always rule?

Voting with 2 choices

Properties:

-    every vote has the same weight
-    symmetry between candidates
-    if a vote for the loser would be changed to a vote for the winner, then no change of outcome.

-    popular vote reflects the total number of votes received by each candidate
-    president is elected by electoral vote
-    each state has  # of senators (2) +  # of representatives many electors
-    electors belong to the party whose candidate won the popular vote in the state (except for Nebraska and Maine). This is a locally winner-takes-all system.
 
• In 1976 Jimmy Carter won the presidency over Gerald Ford with 297 vs 240 electoral votes. The popular votes were 40,830,763 vs. 39,147,973 votes. Contrast the numbers, what kind of percentages do they represent?

-    filibuster: Senators keep talking about a bill they want to prevent until the filibuster is cut off. If the bill is to pass now, it would need to get at least 3/5 or 60% of senate votes.
-    international treaties need a 2/3 majority (super majority) in the Senate.
-    amendments to the Constitution require 2/3 majorities in both House and Senate and then must be approved by 3/4 of the states.
-    veto: a bill approved by simple majorities in the House and the Senate can be vetoed by the President. It then needs 2/3 super majorities in both House and Senate to override the veto.
-    propositions in state elections receiving huge majorities can be declared unconstitutional by the courts.
-    criminal law: need a 3/4 super majority to convict otherwise "hung jury", dismissal of case or retrial.

•  Of the 100 US senators , 57 favor a new bill on health care reform. The opposing senators start a filibustger. Is the bill likely to pass?
• A criminal conviction in a particular state requires a vote of 2/3 of the jury members. On a 12 member jury, 7 jurors vote to convict. Will the defendant be convicted?
• A proposed amendment to the US Constitution has passed both the House and the Senate with more than the required 2/3 super majority. Each state holds a vote on the amendment, and it receives a majority vote in all but 15 of the 50 states. Is the constitution amended?
• A tax increase bill has the support of 70 out of 100 senators and 260 out of 435 members of the House of  Representatives. The president promises to veto the bill. Is it likely to become law?

Voting with 3 or more choices

1992 election results:
 

	Popular Vote	Popular Percentage	Electoral Vote	Electoral Percentage
Clinton	44,909,889	43.3	370	68.8
Bush	39,104,545	37.7	168	31.2
Perot	19,742,267	19.0	0	0
Total	103,756,701	100	538	100

If 65% of the Perot votes had voted for Bush, Bush would have won.

Preference Schedules rank candidatges in order of preference

 

Ballot
1st choice	B
2nd choice	E
3rd choice	D
4th choice	C
5th choice	A

• How many possible rankings can there be for 5 candidate elections?

Ways of deciding the outcome of an election

-    plurality: winner is the candidate with most first place votes.
            A wins
-    single runoff: runoff between the 2 candidates who got the most first place votes.
            B wins
-    sequential runoff:

repeat until only 1 candidate is left:
    eliminate the candidate with the fewest first place votes
    recalculate the table without that candidate

C wins

-    point system  (e.g. Borda count) ( used in College football polls)
        with 5 candidates, the first place earns 5 points, 2nd place earns 4 pts, etc.
        the winner is the candidate with the largest number of points.
         D wins
-    pairwise comparison  (Condorcet method)
        The candidate who wins the most pairwise contests wins.
         E wins

        Condorcet Paradox:

 

First	A	C	B
Second	B	A	C
Third	C	B	A
	14	12	10

 
A beats B in 26/36 votes
B beats C  in 24/36 votes
C beats A in 22/36 votes
who wins?
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