Q:

Simpson Paradox Question

I am trying to understand if the following statement is an example for Simpson paradox:
"In the US elections a certain candidate got more votes than the other, but the other one was elected".
I think it's not an instance of Simpson paradox, but I am having trouble formalizing it. Am I right? if so, how do I explain it formally?

A:

Simpson's Paradox is considered to happen when estimating for some statistical effect between and within groups. In this case there is no factor effect to be estimated, instead you measure a proportion, so I woudn't say that Simpson's Paradox is involved here, but you may consider this as an example of a wider generalized paradox about grouped data. 
To show how there is a relation, let me make a simpler example:
Suppose you have a nation with various electoral district, where which of them elects one candidate (majority system), but some districts are more populous than others. If there is a general tendency within each district population to vote candidate A, but also there is a trend among districts where more populous ones tend to express more votes for candidate B, you could have candidate B take more votes while the victory goes to candidate A.
In Simpson's Paradox usual cases you are interested in within group effects, which are not reflected by analysis that don't take account of grouping, in this case you could say you are interested in elections outcome, which is not reflected by analysis that don't take into account the electoral districts, as if the overall majority decided, which is not.
USA electoral system makes it quite more complicate, but I think I have expressed the gist already. Also, if you think the system should be changed, for what is worth I actually agree, but that's a different story, Simpson's paradox is about data analysis, not about changing the grouping of the data, or changing any electoral system.

