The election system used in the United States can be shown mathematically to be unfair. This page shows the reasons why, and what can be done to correct the problem.
Voters are prevented from voting their real preferences. They can't vote against one choice without voting for another choice. Nobody can vote against all choices and have the vote count. Voters can't vote that they prefer both of two very similar choices. Most of the time, voters are forced to vote against the best choice to prevent the worst choice from winning. Here is the real reason these problems exist: There is a mathematical error in the election process used in the United States.
The voter goes in the booth, and the machine says "VOTE FOR ONLY ONE." When several candidates are equally desirable, the problem is: Which one to vote for? Picking a favorite candidate makes it probable that no desirable candidate is elected. The majority vote desiring one set of issues is split up between many candidates. A candidate with views differing from those of the majority wins, by being the only candidate with those views. The majority view is thwarted, by being split among candidates.
People think candidates are chosen because voters have weird ideas. Actually, there is a BIAS in the election process. It favors candidates that are distinctly different from the others in the race. Here is my conjecture on that bias:
CONJECTURE 1: In any Plurality Voting ("VOTE FOR ONLY ONE") election with 3 or more candidates, probability favors the candidate most different from the others.
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CONJECTURE 2: In Plurality Voting, when two candidates with the same platform run against one candidate with an opposing view, the platform of the two similar candidates can win only if at least one of these is true:
If the voter's preference is not available on the ballot, or a candidate wins for reasons other than a majority preference on issues, it is also not fair. Here are causes of this:
THE MAIN PROBLEM: Voters must be able to vote their real preferences without penalty. The bias against similar platforms must be removed. For years, the method used was to make it hard for thirdparty candidates to get on the ballot. This is not very fair, and does nothing to stop the problem in primary elections. A way must be found to have fair elections with three or more choices.
Plurality Voting ("VOTE FOR ONLY ONE") must be abolished permanently. Voters must be able to have a say on each candidate, independently of the say they have on the other candidates. Plurality Voting is not an independent process; it is a disjoint (mutually exclusive) process. It is guaranteed to have interaction problems.
Approval Voting ("VOTE FOR AS MANY AS YOU WANT") doesn't work either. It gives more power to the voter favoring several choices, compared to the voter favoring one choice has. A way is needed to give each voter the same power in the polls.
Ranking Voting ("PLACE THE CANDIDATES IN ORDER") doesn't work either. It can't tell where a voter stops liking candidates and starts disliking them. A voter could unwittingly vote for a candidate he dislikes.
CONJECTURE 3: "ONE MAN  ONE VOTE" should really mean "one man  one vote per candidate." The voter should have the right to vote on the desirability of each candidate INDEPENDENTLY of his vote on other candidates.
Note that, in the above voting methods, a vote for a choice has much more weight than a vote against a choice. In some of them, you either can not vote against a choice, or you must vote against all other choices. This difference shows the weaknesses of the above voting methods. Unequal weightings of votes for a choice, compared to votes against a choice, cause these biases. This fact leads to the next conjecture:
CONJECTURE 4: To be a fair election system, a vote against a choice must have exactly the same weight a vote for the same choice has.
The biggest defect in Plurality Voting is the unequal power of votes for different choices. This defect must be permanently eliminated in any future election system:
CONJECTURE 5: To be a fair election system, a vote for or against any choice must have exactly the same weight that any vote for or against any other choice has. Also, a vote for or against any political position must have exactly the same weight that any vote for or against any other political position has.
Another problem surfaced when Ross Perot was talked into returning to the race by Bill Clinton. It is possible in the Plurality Voting System to control the outcome of an election by having someone run for that office with a particular platform. Thus, the need to prevent this kind of trickery is obvious:
CONJECTURE 6: To be a fair election system, the entry or departure of a candidate in a race must not have the power to change the outcome of the election, unless that candidate wins the election when running.
Combining these four conjectures leads to a practical solution for this problem:
The voting device, lever, or paper ballot must have three selections for each candidate or issue: "YES," "ABSTAIN," and "NO." If the voter does not make a selection on that candidate or issue, the "ABSTAIN" choice is counted. Selections on one candidate must be entirely free from interlock with selections made on another candidate in the same race.
Compute the vote total for each candidate or issue by subtracting the "NO" tally from the "YES" tally. The highest positive total wins the election. If all candidates have negative totals, a special election with new candidates must be held. If it happens repeatedly on an administrative office, it means the people want the office abolished.
The above forms the basis of the Independent Voting System.
The Independent Voting System ALWAYS chooses the candidate who pleases the most voters.
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Implement these to remove other biases:
ADVANTAGES OF INDEPENDENT VOTING:
DISADVANTAGES OF INDEPENDENT VOTING:
UNFAIR EXAMPLEThree candidates, A, B, and C, run for congressman.

FAIR EXAMPLE:Three candidates, A, B, and C, run for congressman.





Exactly 60% of voters actually voting favor issue X, and exactly 40% oppose it. Who wins the election? Obviously, candidate C gets 40%, or 40,000 votes. The outcome depends on how voters favoring issue X split up between A and B. If either A or B gets over 40% of the vote (40,000 votes), then that candidate wins. If not, C wins. Since a random choice is made between A and B, a binomial distribution is indicated. The mean outcome for either candidate is the number of Voters for issue X, times the probability that a voter for issue X votes for that candidate. That is: 
Exactly 60% of voters actually voting favor issue X, and exactly 40% oppose it. Who wins the election? Obviously, candidate C gets 40,000 YES votes, and Candidates A and B get 40,000 NO votes, from those opposing issue X. The outcome depends on how voters favoring issue X vote on A and B. Since all 60,000 favoring issue X vote NO to opponents, candidate C has a negative total and loses. Since a random choice is made between YES and ABSTAIN, a binomial distribution is indicated. The mean outcome for either candidate is the number of Voters for issue X, times the probability that a voter for issue X votes YES for that candidate. That is: 




That gives an average of 30,000 votes for each candidate favoring Issue X. The variance is the number of voters favoring issue X, times the probability an X supporter chooses A, times the probability an X supporter chooses B. The variance is used to get the standard deviation. The standard deviation is the square root of the variance. We get: 
That gives an average of 54,000 votes for each candidate. The variance is the number of voters favoring issue X, times the probability an X supporter chooses YES, times the probability an X supporter chooses ABSTAIN. The variance is used to get the standard deviation (the square root of the variance). We get: 




Since 99% of all possible outcomes are within 3 standard deviations of the mean in a normal or binomial distribution, the most either candidate A or candidate B can even hope to get is: 
Since 99% of all possible outcomes are within 3 standard deviations of the mean in a normal or binomial distribution, the fewest YES votes either candidate A or candidate B can expect to get is: 




Neither is enough to beat C, so C wins the election when A and B are equally supported. Issue X loses the election. This is the unfair part, because 60% of the voters favor issue X. 
Since 53,779  40,000 = 13,779, issue X wins the election. Rarely would there be an exact tie between A and B, but with a standard deviation of only 73, a revote might be ordered. Fortunately, there are usually minor differences between candidates that will influence the YES vs ABSTAIN choice on each one. RESULTS: 




For issue X to win the election, at least one of these must be true:

For issue X to lose the election, at least one of these must be true:


ACTUAL INSTANCES: Here are some actual cases where this election error has happened:

ACTUAL INSTANCES: Here are actual instances where this fair method is used:

Elections would be much fairer, and would better reflect the will of the voters, if Independent Voting became the only election system used. Follow these recommendations:
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