Remark I'm going to answer this as a formula, but there are many answers that could be given to it.
Formula T = (first_place * a + second_place*b)
Where T is the turtle's score. First_place is the score for first place Second_place is the score for second place a is the number of students that voted for the turtle and gave it first place. b is the number of students that voted for the turtle and gave it second place.
Step Two What is the score that the pet needs to win?
The problem is how many first and second votes were cast by the class? Class total = c*first + d*second. So the Turtle must get more than at least an even distribution which would be T > Class Total / P P is the number of pets. T is what the total must exceed.
There is a further complication. What happens if 2 or 3 pets run away with voting and it becomes a three pet race? That, I think, goes beyond the scope of this question.
Assuming a turtle winning means the declared winner is the weaker one actually won over the stronger one. In this context, the turtle winner is the one who has a lesser number of favourable votes.
The given rules for the points are as follows: 1. Point for the first choice must be greater than or equal to that of the second choice. 2. All points must be positive whole numbers.
Let's suppose we have Henry against Tim. Henry is favourite of the voters and is the leading candidate, according to popular polls. Tim is an excellent manipulator, sly, and everybody knows this.
On polling day, the vote count came out as follows (in point counts)
Henry Tim 2 1 2 1 2 1 2 1 2 1 2 1 10 1 (Henry's own vote) 1 100 (Tim's own vote) ------------------ 17 107 TOTAL POINTS
So Tim the turtle was declared winner of the race, and since everything was according to rule, even a recount of the votes did not change the results.
Be aware, voting by districts (instead of popular votes) also exhibits a similar problem.
