In the build-up to the 2008 parliamentary and presidential elections in Ghana, there have been persistent assertions in the media that the number of votes needed to determine a winner in a presidential election must be 50 per cent plus one vote. This assertion is totally wrong and it is the purpose of this paper to prove why it is a fallacy. First, it will be shown that the phrase "50 per cent plus one" does not appear anywhere in the Constitution of Ghana and can therefore not be used as a criterion to replace the true constitutional provision in determining the winner of a presidential election. Second, it will be demonstrated that the 50 per cent, being a percentage, and the number one, being a real number are non-additive entities and therefore cannot be added as such. Third, the one vote to be added to the 50 per cent will be shown to be non-existent. Finally, it will be shown that in all cases where the total number of valid votes cast is an odd number, no contesting candidate will get exactly 50 per cent of the total valid votes cast in his or her favour, thus rendering the 50 per cent plus one criterion inoperative. The constitutional provision for the election of a President is contained in Article 63 of the Constitution where subsections 3, 4 and 5 state as follows: 63 (3): "A person shall not be elected as President of Ghana, unless at the presidential election the number of votes cast in his favour is more than fifty per cent of the total number of valid votes cast at the election." 63 (4): "Where at a presidential election there are more than two candidates and no candidate obtains the number or percentage of votes specified in clause (3) of this article a second election shall be held within twenty-one days after the previous election." 63 (5): "The candidates for a presidential election held under clause (4) of this article shall be the two candidates who obtained the two highest numbers of votes at the previous election." From the foregoing, it is explicitly clear that there is no mention of the purported “50 per cent plus one" in the Constitution for the election of a President of Ghana. How then can it be used as a criterion for determining a winner of a presidential election in Ghana? For the avoidance of doubt, what the Constitution says in Article 63 subsection 3 is that a winner in a presidential election must have "more than fifty per cent of the valid votes cast." It is as simple as that. This means that a winner in a presidential election may have 50.0001 per cent, 50.002 per cent, 50.1 per cent, 50.2 per cent, 50.41 per cent, 50.9 per cent, and so on. It also means that getting exactly 50 per cent of the valid votes cast in a presidential election does not produce a winner. Indeed, the mandate to become President of Ghana, with the whole country as one constituency, should derive from the support of the majority of the entire electorate of Ghana as indicated in the constitutional clause herein quoted. The constitutional provisions stated above are perfect in all their ramifications. The correct criterion of more than 50 per cent of the valid votes cast for a winner in a presidential election is completely at variance with the purported "50 per cent plus one" assertion which does not exist anywhere in the Constitution. The "50 per cent plus one" assertion is therefore a complete misrepresentation of the true constitutional provision for a winner of a presidential election in Ghana which is simply "more than 50 per cent of the valid votes cast." How the "50 per cent plus one" crept into our political lexicon since the promulgation of the 1992 Constitution of Ghana and the conduct of presidential elections thereafter, only God knows. This notwithstanding and in reality, percentages don't exist in a vacuum or in isolation. A percentage must always be related to a reference base for it to be meaningful. In this case, the reference base is the• total number of valid votes cast at the presidential election. In the process of transformation from real numbers to percentages, the total number of valid votes cast at the election is taken to represent 100 per cent. The percentage share of each contesting candidate is obtained by dividing the number of valid votes cast in his or her favour by the total number of valid votes cast at the election which is then multiplied by 100. It must be noted that in the computational process described above, no reserve pool of valid votes is created for the purpose of adding to any result at a later time. Therefore, after computing the 50 per cent of the valid votes cast, the number one in the purported criterion of "50 pet cent plus one” does not rea1ly exist. The cumulative percentage shares of all the contesting candidates must add up to 100 per cent. This is the litmus proof that all the valid votes cast in the election have been taken into account in the process of the transformation from real numbers into percentage. It further ensures total estimates emanating from this procedure will remain statistically unbiased and fair. It is obvious that to get a percentage share of a candidate in the election one must factor into the calculation the totality of the valid votes cast at the election. The 50 per cent under reference is derivative of the total number of the valid votes cast at the presidential election. A candidate can get this 50 per cent only where the valid votes cast in his or her favour is exactly half the total number of valid votes cast at the election. There is no other way of getting the 50 per cent. Any attempt, therefore, to add one vote or any other real number to this 50 per cent after completing the conversion into percentages will constitute an unacceptable double -counting. In any case, the theory is that percentages can be added to percentages, while real numbers can be added to real numbers, but percentages cannot be added to real numbers since they are non-additive entities. Adding percentages to real numbers will constitute a serious infringement of the fundamental principles of mathematics. In all cases where the total number of valid votes cast in the election is an odd number, no contesting candidate can get exactly 50 per cent of the valid votes cast. For example, suppose the total number of valid votes cast in a presidential election is 121, there is no way a candidate can get exactly 50 per cent of this total. In this and in all such cases, the 50 per cent which is the first component of the purported 50 per cent plus one of the total valid votes cast is impossible to attain by any candidate. The purported criterion of "50 per cent plus one" will thus not be operative. Where there are only two candidates contesting a presidential election, such as in a run-off, an odd number of total valid votes cast will always lead to a winner on the basis of the constitutional criterion. To illustrate this, let us take the total valid votes cast in an election to be 11. In this scenario, there• will be 12 possible outcomes for the 2 candidates as follows: (1l, O); (10, 1); (9, 2), (8, 3), (7, 4), (6, 5), (5, 6), (4, 7), (3, 8), (2, 9), (1, 10) and (0; 11) where the first and second numbers in each bracket represent the number of valid votes cast in favour of the first and second candidates respectively. It is clear from the above possible outcomes that no candidate gets exactly 50 per cent of the total valid votes cast. However, using the constitutional criterion, the first six outcomes will result in a win for the first candidate while the last six outcomes will result in a win for the second candidate. Again, using the previous example with 121 total valid votes cast, there will be 122 possible outcomes; the first 61 outcomes resulting in a win for the first candidate with the rest resulting in a win for the second candidate. Considering an outcome with the first candidate getting 61 votes in his or her favour against votes by the opponent, then the first candidate wins with 50.41 per cent (61/121 *100) of the total valid votes cast. This is in consonance with Article 63 (3) of the constitution. A careful noting of the above process of transformation indicates that having taken the total number of the valid votes cast at the presidential election into consideration before obtaining the 50 per cent of the total valid votes cast, there is no extra single valid vote left anywhere whatsoever for anyone to add to anything in other words; after the conversion into percentages, that single extra vote does not exist. The "50 per cent plus one" assertion as a criterion for winning a presidential election which is gaining currency in the mass media and uncritically adopted by several commentators is absolutely wrong. The time has come for all and sundry to adopt the true constitutional criterion for a candidate to win a presidential election which is more than 50 percent of the total number of valid votes cast at the election." The author is Professor Emeritus, the Omanhene of New Juaben Traditional Area and UN Commissioner on the International Civil Service Commission. Source: Daily Graphic