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I'm working on a tool to analyse how people vote. I have some data with a number of "policies", which are made up of expected votes on different divisions.

So for example, a policy might specify voting "for" divisions 1 and 2 and "against" divisions 3 and 4. I'll write that as {+1 +2 -3 -4}.

Many of the policies in the data set cover the same divisions, and I want to eliminate any that are strict subsets of other policies. So for example, if the above policy is in the data set, and so is {+1 -3}, I'd remove {+1 -3}.

But I also want to eliminate ones which contain the exact opposite votes of a strict subset. So if the data set contains {-2 +3 +4}, I'd want to remove that too.

I want to explain, concisely, what modifications I'm making to the original data set. So I can say that I'm removing any policy which is a subset of another. But how do I describe removing the opposites? Would "anti-subset" be understood, or is there a different term?

Asaf Karagila
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Simon
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    "Anti-subset" is a term which I do not recall to have ever heard. You could call the set ${-1, -2, 3, 4}$ the "dual set" of ${1, 2, -3, -4}$ and say that you remove all subsets of the dual. Note that "dual" is more of a concept than a precise mathematical term. What "dual" means usually depends highly on the context, but would suit your situation. Make sure to define the terms you use precisely. In any case, how would you decide which of the conflicting policies you want to remove? Do you just kick both of them out? – Andreas Lietz Mar 27 '19 at 15:10
  • Ah, "dual" - that's a great idea! In general, I plan to exclude any strict subsets or (thanks again) duals of strict subsets. Exact duals I'm not sure what to do about at the moment. Any other sort of overlap, I'll keep. – Simon Mar 27 '19 at 15:18

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