Certain quarters, including mlq3, have called for a switch to run-off voting in order to ensure that incoming presidents have majorities and therefore stronger mandates. The main drawback here is cost: depending on the particular variant used, we'll be holding at least two elections every time we choose a president. Considering the costs involved in just a single election, and considering that we'll probably end up having two campaign periods as well, this would be very difficult to justify, more so since the advantages of a stronger mandate are hard to quantify. Should this proposal come up for serious consideration, political and economic conservatives would likely oppose it.
As cost is unfortunately an object, the variant we'll probably be considering is the top-two runoff method. In this, only two elections are required, with the top two candidates from the first round going on to the second round. The other two variants, elimination and exhaustive runoffs, often require more than two elections, with the former depending on the number of candidates to be eliminated, and the latter depending on the candidates' coalition building and/or poaching skills.
Still, there's a problem with the top-two runoff method. Essentially, the voters are being asked to decide between the top two first-choice candidates; no consideration is given for getting lower-preference votes (second choice onwards). Thus, there is a significant possibility that a candidate, although not very popular as a first choice, is overwhelmingly popular as a second choice compared to the rest of the field. Such a candidate then could conceivably defeat either of the top two candidates in a two-way race. The rules, however, would eliminate him in the first round, which is a pity since it would be more likely he's a moderate acceptable to a large majority of the electorate, and would probably be able to work more productively with the legislature.
The elimination method, which removes the lowest scoring candidate in successive rounds, would be better in selecting a winner, as it takes into account lower-preference votes. Indeed, it could select a different winner from the top-two method, one more likely to defeat all other candidates in a two-way race. The caveat, as I mentioned above, is that it would require more than two elections. In fact, the number of elections needed is equal to the total number of candidates minus one. Given the number of candidates fielded in recent elections, this method, despite its advantages, is not really economically feasible.
To illustrate these two methods, consider a hypothetical race with four candidates: FPJ, Lacson, Roco, and GMA. They get 35%, 25%, 21%, and 19% of first-choice votes respectively. Using the top-two runoff method, Roco and GMA are immediately eliminated, and voters are forced to choose between FPJ and Lacson. Of the 40% total who voted for Roco and GMA, assume 18% are willing to support Lacson either as second or third choice, 9% would vote for FPJ, and 13% would abstain. Results for the second round would thus be 44% for FPJ and 43% for Lacson. If we don't count the 13% who abstained, that would be 50.6% for FPJ and 49.4% for Lacson. Using the top-two method, FPJ wins.
The elimination method yields a different result. In the first round, GMA is eliminated. It's not farfetched to assume that most of her supporters would have Roco as their second choice. Thus we can postulate that of her 19% base, 15% would go to Roco, 2% to Lacson, 1% to FPJ, and 1% would abstain. The second round results would thus be 36% for FPJ, 27% for Lacson, and 36% for Roco, eliminating Lacson. Of Lacson's 27% total, perhaps 2% would abstain, 13% would go to Roco, and 12% would go to FPJ. Final round results would thus be 48% FPJ and 49% Roco. Leaving out the 3% total who abstained, we'd have 49.5% FPJ vs 50.5% Roco. With the elimination method, Roco wins after three rounds. This is arguably a more accurate reading of the electorate's collective intent.
The top-two runoff method is unfortunately only marginally better compared to plurality voting. The sole advantage gained is the certainty of a majority for the winner. As we noted, it fails to take into account voters' second and third choices (as well as all subsequent preferences). By combining an emphasis on first-choice votes with a high cutoff requirement (as only the top two are selected for the second round), candidates are rewarded for staking out relatively extreme positions that appeal to a sufficient portion of the electorate who can give them their first-choice votes. Moderates, while acceptable to a larger portion of the electorate (as second or third choice candidate), would lack a large enough base of first-choice votes to advance to the second round. They are inherently disadvantaged by this system.
In any case, the advantage of a majority is dubious anyway if turnout for the second round falls significantly. Is it still a strong mandate if a large number of voters found both top-two choices unacceptable?
The elimination method, by getting rid of only one candidate at a time, allows a greater range of voter preferences to come into play. Second and third choices, even fourth or fifth, can affect the outcome significantly. There is a relatively higher tendency for the more moderate, more generally acceptable candidates to be selected. If we consider that such people would likely be able to work with Congress more effectively, then this may be the better method. Unfortunately, there's the cost. If only there was a way to do this more cheaply...
Next, we look at instant run-off voting...