1. A summary of the result from the 2016 referendum on membership of the European Union is given in a text box to the right.  Show that the percentages for these elements is as shown: (i) Remain 48% (ii) Leave 52% (iii) turnout 72.2%. Find the margin of 'decision'  as (iv) the number of votes (v) as a percentage of the electorate and (vi) as a percentage of those who voted. Use 4s.f. for the percentages. Find the margin of disagreement, the percentage of the difference in votes in the valid votes.

2. The 1975 referendum, on almost the same question, asked for a Yes/No decision on staying in the EU, which we had joined at the start of 1973. Find (i) turnout, (ii) percentage for Yes in the vote (iii) percentage for Yes from the electorate (iv) the margin of disagreement.

3. Wikipedia's presentation of the 2016 result says the Leave percentage was 51.892%. The corresponding page for the 1975 result says the Yes percentage was 67.232%. (ii) Explain what has been done.

4.  If we assume that the proportions of votes (Yes / No / invalid) was correct for the whole electorate, what % turnout was required in 1975 for an absolute majority decision? Repeat this for the 2016 decision, explaining why such a turnout is unlikely.

5. If we look at who chose not to vote or to make an invalid vote, we have a measure of the indifference to the result, which may be for any number of factors, from illness to anarchy or nihilism. If I say the 1975 indifference figure was 35.5%, what do you say the 2016 figure was?

 I made a general spreadsheet to solve these problems. I used Create Names and have shown the formulas, not the values. If you had a set of numbers for a different vote you could generate a set of response to similar questions quite quickly - you have only four numbers to input.

6.  in 2012, Puerto Rico held a referendum over its territorial status (it is the Commonwealth of Puerto Rico, a territory of the US but not a state). There were two questions: Should their status continue as it was (so 'No' indicated a wish for change) and which of three non-territorial options did they prefer, statehood, free association or independence.
There were 1,363,854 valid ballots and 515,348 blank and invalid ballots. So
votes and valid votes are dramatically different. In a previous referendum, one option was None of the Above (NotA. not-A) and I suggest here that the many blank ballot papers were a result of that history. On the first question, 970,910 voted No and 828,077 voted Yes. of those who answered the second question (because you might expect the 'Yes' group to ignore it, as recommended by the Popular Democratic party), statehood had 834,191, association had 454,768 and 74,895 went for independence, with blank 480,918 and rejected 18,357. The registered voters numbered 2,402,941.

 What would you have published in an unbiased report?   I've given you a table of results much as above. Indicate which % figures you think are the most helpful in understanding the situation, with explanation where you think that is appropriate. 

Make an argument for what attitude you would take to the result - if you were a political thinker, what route would you take in support of your perception of the result?

President Obama had said that he would support the will of Puerto Ricans if there is a clear majority. USA Today, 20121107.  What would you have recommended to the President as a result of this ballot? Write a paragraph of explanation.

If you had had a vote at the time, how would you have filled in the ballot paper? 

DJS 20190214

Valentine's Day in the Year of the Pig; Zhu Nian 猪 年。 

1. 16141241+ 17410742 + 25359= 33577342 votes cast, 33577342 /46500001 = 72.209% = 72.2%, (iv) Leave - Remain = 1269501 = 3.781% of votes = 2.730% of electorate. (vii) margin of disagreement is 1269501/33551342 = 3,784%, not the apparent 4%. That is 2.73% of the electorate, those who could possible have voted.
Check: 51.9%-48.1% = 3.8%. 3.78% * 72.16% = 2.727% 

2. Turnout was 64.482% (64.5%) Yes 67.1% of votes, 43.35% of electorate. Margin of disagreement is  34.5% of valid votes, or 22.22% of electorate.

3. The votes cast is different from the valid votes cast. Wikipedia has been consistent in calling the vote as a percentage of valid votes cast. That makes no distinction between an invalid vote and failing to vote. An Australian would complain, as they are required by law to vote, so that making an invalid vote is a measure of protest, not a measure of indifference or disinterest.

4. Need for 4006667/2 + 1/2 = 2004339 Yes votes so turnout must increase by a factor of 2001339/17378581, => 64.618*200/174 = 74.526%, call that 74.5% or 75%. The invalid votes have a significant effect. For 2016 the required votes for Leave is 23,250,001, which at a continued 51.853 % (not 51.892%) moves turnout from 72.209% to 96.427%. Recognising that this is over 95% is enough. the highest turnout for any election or referendum was 83.9% in 1950. In Australia (with compulsory voting since 1924) turnout stays between 91% and 96%. So even by making voting compulsory, it is unlikely we could have had an absolute majority decision, the margins are that close. You could therefore expect that a small change in national opinion would have a significant effect of the result. Or, to turn that around, one could be very annoyed with those who were eligible to vote but did not vote.

5. (electorate - valid votes) / electorate = 12,948,018 / 46500001 =  27.845%

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