Ireland has a pretty good voter registration system; people are sent registration cards as their 18th birthday approaches, and most houses are canvassed by polling registration workers every 3 years or so, and it's also very easy to register.
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Each constituency has its own returning officer, and is handled in its own fenced off area. The fence is in a square, with count staff and their tables on the inside of the fence, and observers can line up on the other side of the fence.
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Each ballot box is opened in public view, and the votes are taken out one by one, unfolded and turned to face the observers. At the same time, the observers are chaotically crowd-sourcing a tally.
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Basically observers are handed sheets of paper and add a tick for every candidate they see a "1" vote for. By the time all of the votes have been unfolded, the observers have a very accurate count of who got how many "1" votes.
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Experienced tallymen also have sophisticated models in Excel spreadsheets that use this to forecast how many "2" , "3" votes and so on the candidates will get, and make projections for TV, Radio and so on to use as news.
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Then the actual count starts! In Ireland each constituency (except the Presidency or a special election) has multiple seats, and we use a system called Proportional Representation by means of a Single Transferable Vote (PRSTV) to elect each seat.
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You take the turnout of the constituency, divide it by the number of seats, add one, and that's the "quota". A candidate is elected if they reach the quote. Some reach it on "1" votes alone. They get right in!
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When a candidate reaches the quota, all of their ballots are then re-counted but looking at the "2" votes. These votes are then distributed to those other candidates, in proportion to the elected candidate's surplus (the number of votes more than the quota they got).
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That raises the total for the other candidates, and maybe they reach the quota, and the same thing happens for them. Otherwise, the candidates that can't possibly be elected are eliminated, and the next preferences from their ballots are redistributed.
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This means there can be as many counts as there are candidates. It usually takes all day, sometimes 2, and that's before recounts! But it's worth it, it means that people's votes are never "wasted". Your vote can always go to someone.
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A few other things: some ballots are spoiled - some observers and representatives from parties adjudicate on these. Unclear votes are discarded, votes with identifying marks can be argued over. Generally returning officers want to favor including them than excluding.
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There's a media moratorium on polls in the 24 hours before an election, a period of reflection. And there's a referendum commission who writes neutral advice on the referendums and sends it to everyone. http://refcom.ie for their take on this week's.
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Ireland's turnout rates haven't been great for the past 20 years or so, but in general it's still a pretty robust democracy. As I write, my parents are out canvassing and knocking on doors to encourage people to vote! /end
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