Dealing with people's uncertainty in opinion poles

When asked about their voting preferences, some people will answer with honesty that they definitely do intend to vote and that they have absolutely made up their mind who to vote for. Other people will answer that they will probably vote and that they will most likely vote for a given candidate, but could possibly be persuaded to change to another between now and election day. For the polster, it may seem tempting to treat those who say they will most likely vote for a given candidate the same as those who say they will definitely vote for that candidate. However by ignoring that stated uncertainty, some useful information is being thrown away.

Suppose a polster were to ask a member of the public "will you vote in the next election?" The repondent could be given a list of possible answers to chose from: definitely yes, probably yes, probably, may be, definitely not. Those answers in natural language can be converted to apropriate probabilities. When we combine all the answers we can find the expected number of respondents who will vote.

We can also ask the respondents the likelyhood that they would vote for each of the candidates. It would be wise to offer answers in English rather than as probabilities, since some people won't be familiar with probabilities. From the answers, we can then obtain estimates for the probabilities that they will vote for each candidate, conditional on turning up and voting on election day. We can combine (multiply) the probability of voting (at all) with the probability of voting for a given candidate (conditional on voting) to get the overall probability that respondent (r) will vote for a candidate (c), we'll denote this probability P(r,c).

The expected portion of votes for candidate c will be: \[ V(c) = \frac{ \sum_{r=1}^{n} P(r,c)} { N } \] where n is the number of respondents
and the expected total number of votes that will be cast by our respondents is calculated: \[N = \sum_{r} \sum_{c} P(r,c) \]
For example, suppose we examine the answers from a respondent and we deem there to be a 20% chance that she will not vote, a 60% chance that she'll vote for candidate 1 and a 20% chance that she'll vote for candidate 2. Rather than treat her as a full supporter of candidate 1, we can use those probabilities as her contribution to each outcome.