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I've been struggling to parse the following sentence from the UK petition to implement EU Referendum Rules triggering a 2nd EU Referendum.

We the undersigned call upon HM Government to implement a rule that if the remain or leave vote is less than 60% based a turnout less than 75% there should be another referendum.

I'm puzzled at the phrase "less than 60% based a turnout less than 75%". If it were something like "less than 60% based on a turnout of less than 75%", I wouldn't have any trouble, but apparently it isn't. Especially the usage of "based" like this, without any preposition, seems quite unfamiliar.

How should I parse and understand the sentence?

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    As an AmE user, I would think it should be based "on". But it is possible that BrE users have a peculiar way of using a that AmE users do not. I doubt it, but I would like to see what they say. – Em. Jul 4 '16 at 8:44
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    It amuses me that four million people have signed a petition the text of which is incoherent. – Colonel Panic Jul 4 '16 at 12:25
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    "based [on] a turnout less than 75%" bbc.co.uk/news/uk-politics-eu-referendum-36634407 – Colonel Panic Jul 4 '16 at 12:26
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    @probablyme: A petition to parliament written by some randomer on the internet :) It has all the editorial oversight (formal or otherwise) of a Facebook status – Lightness Races in Orbit Jul 4 '16 at 16:05
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    @ColonelPanic Maybe that means that four million Brits were able, like ourselves, to work out that the word "on" was missing, thereby rendering the text coherent, see the value in the proposal, and add themselves to the petition. – BobRodes Jul 4 '16 at 17:22
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In fact it needs to read "based on" (or "based upon"; see comments).

As you indicated that you expected, base on is a phrasal verb here. It is a multi-word item which has a meaning like using in X is calculated using Y. It cannot retain this meaning if the on element is omitted. It's obviously a typo.

http://www.macmillandictionary.com/dictionary/british/base-on

It would also be more common in standard English to include of in a turnout of less than 75%. However, leaving it out is acceptable. In this case, of is a word, a preposition, that stands on its own. It is not so tightly attached to another word like on is to based in based on. It would be understood that a turnout less than 75% equals a turnout [that is] less than 75% or a turnout [of] less than 75%.

We can see that on has been added to the text here and, here, and here.

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    Can you maybe add an explanation to this? – Nathan Tuggy Jul 4 '16 at 9:04
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    Like, We don't use based that way without on? – Jim Reynolds Jul 4 '16 at 9:26
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    The OP indicates that they would understand it with the missing on. I am answering that the on is required. – Jim Reynolds Jul 4 '16 at 9:49
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    I would use "upon", but that may be just my middle-aged BrE. – Klors Jul 4 '16 at 14:58
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    @Klors Ah, I had not considered upon. I don't think it's any more correct, but perhaps more precise and more formal. I'll add that to the answer. – Jim Reynolds Jul 4 '16 at 15:09
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I am a British English speaker.

I think the person who posted the online petition just accidentally made some grammar mistakes because they created a petition in a hurry, and the website offered no feature to correct the grammar later. The petition was posted very shortly before the final result of the voting was announced. Perhaps the poster thought that, by posting before the final result, the petition had a greater chance of being accepted. That was perhaps why they hurried and didn't check their grammar.

The correct usage should have been: based [on] a turnout [of] less than 75%

The [on] is absolutely essential. The [of] is optional, but usual usage.

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