A majority victory is not that impossible

By this time next week, we’ll already know the true vote intentions of Brazilians towards the candidates running for president. Not long time ago a runoff was taken as grant, but last polls have been converging on the feeling that Brazilians are about to reward the Workers’ Party’s government another term.

Marina Silva (PSB), who became the “salvation” for those discontents with the way politics is done in Brasilia for 12 years, recently began to fall in the polls, causing some to ask themselves if she can make it to advance in the runoff. Perhaps, the important question with the latest flows in public opinion is whether Workers’ Party’s dream of winning the presidency by a majority, is tenable or not.

Although the odds are for a runoff starting next week between Dilma and who ever takes the second, Dilma has a shy but increasing likelihood of avoiding it. For instance, if Dilma manage to drain out 4% of the opposition’s vote over this week, say 2.5% from the runner-up candidate, Marina Silva, who is already falling according the polls, and 1.5% from the Social Democrat, Aecio Neves, who is currently recovering from the pre-Marina stage, while keeping the distribution of undecideds as is–proportional to the candidate’s actual support, Dilma can make it. At least is what we can interpret from the chart bellow.

This graph uses data from simulated elections (10k) based on the last polls. According to this model, if the election were held today, Dilma would win 42% of the popular vote, Marina so 29%, Aecio 19% and others, including wasting vote: 10% Then the histogram shows the marginal difference between Dilma vs all the others, and is computed as a Beta distribution of “successes” and “failures” of having more than 50% of the votes.

What does this tell us about the difference in vote support for government vs opposition? The important stuff here is that the threshold of zero (0), meaning no difference or 50/50 vote distribution is in the tail of the curve, but out of the rejection region. Actually, it is half away from the center of the curve, the point where the probabilities are null. Therefore, I’d not totally discard a majority victory, although it is tough to do in one week what the government candidate should have done over the campaign.