Binary Neural Network Classification or Multiclass Neural Network Classification? I am confused about the difference between a binary and multiclass neural network classification. If I am writing an algorithm that has 2 output classes (Obama or Romney), but not yes or no (so not like Obama or not Obama), then is it a binary neural network or a multi class (2 class) neural network classification?

What I do know:
A binary neural network classification outputs 1 unit. If a multi class classification neural network has k classes, then it has k outputs.

What I think:

I think it is a binary neural network classification because I am really only trying to output one thing, whether a county votes for Romney or Obama. I am confused because I thought binary was more like Romney or not Romney classification and I am not sure if that is the same as Romney or Obama. Just wanted to double check and clarify my understanding.
I think you are making things more confusing then they are. 

Binary

In this case you have two possible outputs: 


Obama = 1. 
Not-Obama (who in this case can only be Romney) = 0. 


Multi-Class

In this case you have k possible outputs, for example when k = 4: 


k = 0: Obama
k = 1: Romney
k = 2: Clinton
k = 3: Bush


There are approaches to tackle multi-class classification as binary classification which are called One-vs-rest classification and One-vs-one classification, other classifiers, such as Random Forests, are able to deal with a multiclass setting in a natural way. For a brief report, see here.