Biden and Trump

Find a formula  

Suppose Biden and Trump stand for election to a golf club which has a hundred members. The one among them who gets more votes would be accepted as a new member. Sometime during the counting, the secretary of the club comes out and says that one person has got 49 votes and the other has got 36 votes as of that moment. The remaining votes are being counted. Someone says, since one has already got 49 votes, why don’t we stop the count and declare him the winner?  The Secretary says, "No. we have to be mathematically sure that one candidate has such a lead that he canot be defeated if the election continues".    

Let H be the votes earned by the leading candidate by that time.

Let L be the votes earned by the other  candidate by that time.

The total number of votes distributed, one per member = 100

Please note all members may not vote. Write the stopping condition in terms of H, L or both.  If the condition is satisfied, we should be able to stop the counting and declare the candidate with H votes the winner of the election.

Examples of conditions that are not good:   

                     H > L                  is not a correct stopping formula.

                     H + L < 100       is not a correct stopping formula.

Now comes a second problem. Assume that there are three candidates in an election. Only one candidate is to be elected. Can you find a stopping formula that says when the leading candidate is sure to win. 

Srinivasan Ramani   

6-Nov-2020  

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