Imagine precinct-level data on voting records.  The outcome variable is binary, depending on whether a voter selected the Republican candidate.  A colleague hypothesizes that voters in larger precincts are more likely to vote Republican and wants to include the number of voters as a predictor.  In other words, the predictor variable and the denominator in the proportion would be the same, as in this lme4 code:

Proportion.Republican <- glmer ( cbind (Votes_Republican, Number_of_Voters) ~ Number_of_Voters + (1|Precinct), family = binomial)

This seems strange to me, but I'm not able to explain why it wouldn't work.  Any advice?
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