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New Zealand recently voted on a potential new design for their flag. The question was:

"If the New Zealand flag changes, which flag would you prefer?"

The five options were chosen by a government appointed committee: enter image description here

As you can see the first option and last option are the same design with one of the colours changed.

Preferential Voting was used - and explained here.

It has been suggested that as voters were asked to rank their options in order of preference and the first/last options are basically the same flag the outcome was heavily skewed in their favour.

Can someone please explain how the outcome is affected by having two almost identical options in a Preferential Voting system?

In case you're wondering the first option won.

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    Preferential voting is also known as instant runoff voting. You might be able to find something to explain it by searching on that. My guess is that people will tend to assign those two flags adjacent values, which may affect the results. Not quite sure how the results would work out on that, though.
    – Bobson
    Dec 13 '15 at 21:36
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    This is a question which is not so much about politics but morer about psychology. Definitely an interesting topic, but I am not sure if this is the right stackexchange for such questions.
    – Philipp
    Dec 13 '15 at 23:15
  • @Philipp yes, I wasn't sure where to post it to be honest. Could it also be posted/ answered in "Cross Validated"? If the mods think there's a better Stack Exchange I'm fine with it being moved. Dec 14 '15 at 0:09
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    en.m.wikipedia.org/wiki/Voting_paradox indicates that all voting systems fail at least one intuitive precondition for a "fair" election system. Dec 14 '15 at 0:56
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    @Philipp, I think this question has great relevance for politics. It's a general question about how a well-known voting system, used in several countries' political systems, works in practice. The particular example used to illustrate the situation of two very similar options skewing an election happens to be the choice of New Zealand's flag but it could equally apply in many situations. (The choice of New Zealand's flag is also of intrinsic political interest. Symbols are a very important part of politics.) Dec 15 '15 at 7:47
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In preferential voting, it is possible that two similar options split votes which a single option could have accumulated. That could result in a less desirable alternative to be chosen instead. However, this only happens when a substantial number of voters only rank one of the similar options and don't bother to rank the other one.

Apart from that, it's really hard to tell how the absence of one of the similar flags would have affected the results, even from a mathematical point of view. The only voting system which is paradox-free is majority vote on two alternatives, and even this system can be skewed when human psychology factors in.

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This "Preferential Voting" is more accurately known as instant-runoff voting. (There are other preferential methods, too.)

As that page says:

The independence of clones criterion states that "the election outcome remains the same even if an identical candidate who is equally preferred decides to run." IRV meets this criterion.

So having multiple similar flags on the ballot should not augment nor harm their chances (the way they would in a plurality election, which is called vote-splitting).

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