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For example today, the different states got called at various points of the day. Probably the decision to call has something to do with the margin of current count and the current percentage of reported votes, but I'm not able to infer a clear pattern. Is there a formula, or is it a judgement call by the network's experts?

  • This whole process seems quite foreign to us in the UK, where local government officers actually count the voting slips (no machinery involved), and a person called a returning officer stands at a podium and announces the results, for each of the 650 constituencies. Even so the result for the whole country is usually known within about 4 or 5 hours of the polls closing - unless it is very close. Do they announce the actual counted results in America? – WS2 Mar 9 '16 at 23:20
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It's a judgment call.

They tend to use a combination of exit polls, voting results, and expectations. For example, if a lot of returns have come in white neighborhoods and most black neighborhoods have not returned results, they might expect that Hillary Clinton's results will improve. However, if things are switched the other way, then Bernie Sanders could be expected to improve. If all the data are in line, they'll call earlier than in a race where there is more conflict in the data.

Relevant link: http://ajrarchive.org/Article.asp?id=519

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