Ultrafilters are typically described and used as highly abstract set theoretic objects that just happen to have several very nice properties. This talk will arrive at the definition of an ultrafilter by analyzing what types of voting systems have certain nice properties. We will then use the intuition that ultrafilters are "good" voting systems to describe ultralimits and ultraproducts as the results of voting in particular contexts. No prior knowledge of ultrafilters or their many amazing uses will be assumed.