Voting Data
The results of the 2000 election should be examined in terms of different methods of counting, which are expected to produce different results.
Table 1 – Results of the 2000 Presidential Election in Florida
Application of Different Voting Methods
The Plurality Method
From the Plurality Method, the winner is Bush, who has the most votes compared to the other candidates (Pirnot, 2019). For the other methods, reasonable assumptions must be used about how voters would rank the candidates if that were possible. This uses assumptions in ascending order; that is, if 2,911,872 voted for Bush, 2,910,942 for Gore, 97,419 for Nader, and the least number of voters for Buchanan, 17,472, then the following distribution of preferences is actual.
Table 2 – Distribution of Voter Preferences
The Pairwise Comparison Method
Using the Pairwise Comparison Method, it can be determined that Bush retains the lead because he scored three points versus two points for Gore and one for Nader. Since Bush beat each candidate in head-to-head comparisons, Condorcet’s criterion is satisfied, i.e., Bush is the absolute election winner.
The Borda Count Method
Bush also wins The Borda Count Method, scoring 20,724,987, while Gore scores only 20,609,166.
The Plurality-With-Elimination Method
The Plurality-With-Elimination Method could not have been used because there were no second votes. However, in this case, Buchanan should have been eliminated as the lowest vote-getter, and a second round should have been held. Then, we should look at the outcome and decide if a third round was necessary.
Assuming that a minimum of 51% is required to win, which would count as a quota, neither Bush nor Core individually could reach that quota, but together they could. However, the quota can also be obtained by Bush and Nader together, who will get 51% together. Hence, all three candidates have veto power, but Buchanan does not. It is noteworthy that Bush, although he was the winner of the election, was not a dictator since he did not have the maximum power concentrated in his hands compared to the other candidates. Only Bush, Gore, and Nader are critical since leaving any of them in joint coalitions would cause such coalitions to cease to be winnable.
The Banzhaf Power Index
In terms of The Banzhaf Power Index, all three candidates except Buchanan also had the same 33.3%.
The Shapley-Shubik Index
The Shapley-Shubik Index was also calculated for each candidate. The results showed that Bush and Nader had maximum scores of 33.3%, with Gore having 29.2% and Buchanan having 0%. This means that Bush and Nader had the most influence on coalitions because they were more likely to lead them to victory than the other two candidates.
Reference
Pirnot, T. (2019). MyLab Math for Mathematics All Around — 18 Week Access — plus Third-Party eBook (Inclusive Access) (6th ed.). Pearson – Channel Partner Integration.
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