These are just some notes I scribbled down the other day. I'm not a statistician (as will become clear very soon*) but I did want to dig into the opinion poll results a little more and try to work out how they could translate to an actual referendum.

NB – I base everything on the idea that the same electorate would vote as in elections to the Catalan parliament. It's not clear if this would actually be the case. E.g. if legal foreign residents or 16 & 17 year-olds were allowed to vote, that could well skew things significantly. I'm not sure of the chances of either of those happening but they have been hinted at previously.

**If anyone better qualified than me can find critical errors or malpractice in my shaky workings, please let me know: I'd like to be better at this sort of thing.*

==

Catalonia independence. Poll (#CEO): YES 55,6%, NO 23,4%, ABSTENTION 15,3%. In Catalonia, the referendum is still forbidden by Spanish gov.

— Carles Costa (@carlescostatv3) June 20, 2013

Numbers

1% = 54138,50

5413850 electorate

YES 55.6 3010100

NO 23.4 1266840

ABS 15.3 828319

Election results ONLY ever count those who vote.

Which means, of those who would vote (4276940) 1% = 42769.4

**YES 70%**

**NO 30%**

** Which is a major victory for the YES vote.**

But that's based on CEO numbers from May which might not be accurate anymore.

I should apply the same standard to these: http://www.cadenaser.com/csermedia/cadenaser/media/201309/11/espana/20130911csrcsrnac_1_Pes_PDF.pdf

In this case, I assume the same electorate to make things easier. However, it remains unclear just how many people would be allowed to vote.

1% = 54138,50

5413850 electorate

YES 52.3 2831443.55

NO 24.1 1304737.85

DK 13 703800.5

ABS 7.7 416866.45

We discount the Abstentions.

Sum all votes (Yes, No, Don't know): 4839981 (1% = 48399.819)

Of which

Yes: 58.5%

No: 26.9%

DK: 14.5%

Even if ALL Don't Knows voted No, the No vote would only have 41.4% of the vote, compared to 58.5 (a 17.1 % point lead to the Yes vote). If only half voted No, and half voted Yes, the balance would be:

**Yes: 65.75**

**No: 34.15**

**This is a 31.6 % point lead to the Yes vote.**

Accordingly, it appears that** the Yes vote would win a referendum on Catalan independence by something between 17 to 40 percentage points**, the lowest lead representing a situation in which every voter who responded 'Don't Know' ended up voting No, which strikes me as unlikely.

Your calculations are correct. It's simple arithmetic.

We have A, B and C, which are the percentages of people who say would vote yes, no and abstain respectively. Now, let's say N_a is the number of people who say would vote yes and N the population. Then

A = N_a / N

and we want to find A' such that A' = N_a / (N_a + N_b), i.e. the percentage of people who would vote yes over the population leaving the abstainers out. A' can be expressed in terms of A and B:

A' = N_a / (Na + N_b)

= (N_a / N) * (N / (N_a + N_b))

= A * (1 / ((N_a + N_b) / N))

= A * (1 / (A + B))

= A / (A + B)

Likewise, B' = B / (A + B)

So, if we take the CEO data, A' = 55.6 / (55.6 + 23.4) = 0.7037975 and B' = 23.4 / (55.6 + 23.4) = 0.2962025.

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