Logistic vs. OLS So the title is a bit misleading.  
I have a categorical dependent variable (no, maybe, yes) in multiple observations over a span of several years that I have turned into "percentage that said 'yes'"  So technically it is now "yes" vs. "no and maybe" and bounded by 0 (0%) and 1 (100%).  I am using OLS because I am interested in the one unit increase association between my independent (another percent) variable and my dependent variable.  None of the coefficients of my independent variable would result in my dependent variable crossing 0 (0%) and 1 (100%).  Additionally, besides the loss of interpret-ability, I don't want to use logistic regression because the "prevalence" of my independent variable is very high (>65% in most cases), so the resulting OR from a logistic regression would be inflated.  What do you all say?  How would you explain the use of OLS in this case if someone was very adamant that I have a dichotomous outcome variable?  
 A: You would not validly explain the use of OLS:


*

*If you interpret the OLS outcome as probability of outcome = 1, then your model says that it is possible for P$(Y=1) > 1$, and for P$(Y=1) < 0$, which is problematic.

*Your errors are not distributed $\mathcal{N}(0,\sigma)$, thus violating a fundamental OLS assumption.

*Although you write "None of the coefficients of my independent variable would result in my dependent variable crossing 0 (0%) and 1 (100%)." This seems patently false, although unintended I am sure, for any value of $\beta \ne 0$: your model must cross both $Y=0$ and cross $Y=1$ (regression lines are infinite): what is your OLS model's best guess as to the probability of $Y=1$ when your model says the probability is less than or equal to zero? (And vice versa?)
You write "I am using OLS because I am interested in the one unit increase association between my independent (another percent) variable and my dependent variable." You seem unaware that logistic regression is interpretable. With logistic regression you can:


*

*answer the question "What is the change in $\ln(\text{odds}(Y))$ (the log odds of the probability of my dependent variable equals 1) given a 1-unit increase in my independent variable," or, if your prefer to talk about relative probability, rather than log odds, you can 

*interpret $e^{\beta}$ as the answer to the question "What is the change in odds$(Y)$ given a 1-unit increase in my independent variable."


As user777 has noted: you are misinformed about logistic regression and high (or any) prevalence biasing odds ratios.
A: As others have said, OLS is inappropriate in this setting.  It is also completely inappropriate to discard valuable information at the outset by pooling "no" and "maybe".  The original problem is calling for an ordinal response (3-level) model such as the proportional odds logistic model or the log-log link cumulative probability model (discrete proportional hazards model).
To try to achieve interpretability by choosing a wrong model whose every assumption is violated is not a good idea.
