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 the remaining others, including wasting vote: 10%. The histogram shows the marginal difference between Dilma vs all 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.

Three major polling houses published their polls this week: MDA, Ibope, and Vox Populi. The following numbers incorporate these data. With current data, a runoff between Dilma and Marina seems to be inevitable (.87), though its certainty has decreased from the previous week as the following chart indicates.

How to understand the following plots: The big dot at the end is my best guess where, I think, the candidate will end. The "plus" signs represent the polling data estimates published by polling houses.

DILMA ROUSSEFF (PT)

MARINA SILVA (PSB)

AÉCIO NEVES (PSDB)

OTHERS

For those who follow this tale, the chart below shows the hitherto of vote intentions among the viable candidates as reported in various polls. Data collected over 2012 were simply disregarded and those from 2013 enter in the model as prior values (covariance) for the 2014 estimates. The big dots at the end of the graphs are my best guess where a particular candidate will end. The "plus" signs represent polling data estimates.

Neves (PSDB) shows a drift reaction in the last polls, in association with Marina's falling the gap between them narrows. Although this trend is not clear across all polls, one major national polling house – Ibope has picked it up with intense this week.
Perhaps most importantly, while Marina turns down, the polls suggest the government is recovering and has now the same share as in April this year. It's this trend I'd like to pay attention over the coming two weeks. If the big move in sentiment towards Marina (PSB) captured by the polls over the last weeks is genuine or ephemeral.

Finally, the undecideds are still significant in number: 8%, which means about 11 million of fellows. So, this stock of voters may play a role in the final spin of the campaign. Actually, who decide now, tend to be consistent and avoid decision costs bringing her decision to the runoff if her candidate succeed the primary.

DILMA ROUSSEFF (PT)

MARINA SILVA (PSB)

AÉCIO NEVES (PSDB)

OTHERS

Yesterday, more Scots than ever since universal suffrage was introduced cast a ballot on the matter of independence. The turnout was itself phenomenal and that implicating a series of questions for the government authorities and citizens, but for the time being the sole question was: would this benefit one side or the other? The verdict favored the "NO"--better together--by a margin little higher than indicated by major polling houses over the last week. And this returns to the point I raised roughly a month ago: the evidence from political science literature suggests that voters who failed to promptly decide are more likely to vote for the status quo in referendums like this.

Just few hours before Scots head to the polls, there is not an overwhelming advantage of the anti-independence vote. Actually, the margin is shorter than last time I looked at it, but despite such a growing trend in favor of the "Yes" campaign in the last weeks, the "NO" side has an edge still. To frame this in terms of probabilities that $\theta_{No}$ exceeds $\theta_{Yes}$, I write a short function (replicated here) that will use simulation from the Dirichlet distributions to compute the posterior probability that "No" exceeds "Yes" shown in the lovely chart below.

The data used here to draw the distributions were gathered from a series of polls and available at the wikipedia. The polls employ different methodologies and phrase questions differently. For instance, some surveys ask respondents how they would vote if this referendum were held today, others ask them how they intend to vote on 18th September. By aggregating them, any swing could be the by-product of the random variation to which all polls are subject.