Getting to the core of problem
For a secret ballot, a question of the form “Do you want this apple?” was selected.
The two alternatives offered were 1. ‘Yes’ and 2. ‘No’ (i.e. 50 per cent + 50 per cent = 100 per cent).
The question was not in the form “Would you take this apple if.... ?”.
No further action was taken. Two years later there were doubts of the most suitable appropriate action, based on the simplicity of the original question. It was therefore decided to run a further more detailed ballot of the form “Would you take this apple if.... ?”.
Three of many possible alternatives were offered: A. Yes, if you give me only the apple you are offering, B. Yes, if you immediately replaced it with a fresher apple, C. Yes, if you immediately replaced it with a pear. However, it is clear that the second ballot had absolutely no connection to the first.
Since question ‘A’ had one part (original object and no further action required) and questions ‘B’ and ‘C’ each had two parts (object plus further action required) the actual weighting of the questions was 20 per cent + (20 per cent + 20 per cent) + (20 per cent + 20 per cent), equalling 20 per cent + 40 per cent + 40 per cent = 100 per cent.
This also ensured that (however the three questions were answered) ‘A’ could not be an outright winner unless every paper returned was marked ‘A’, since the marking was actually awarded as 33.3 per cent + 33.3 per cent + 33.3 per cent (leaving a recurring fraction, representing the missing ‘if’).
As there was money to burn the ballot went ahead.
It would have been much easier to run the ballot along the usual lines when offering the illusion of choice, i.e. mark the ‘X’ on the paper and offer the ‘voter’ the choice of paying for postage to return it to sender or returning it to the sender online (without allowing the box to be changed, meaning that sending equals agreement).
The result is always the same, since the extra section marked ‘Your opportunity to express your opinion’ can never be used to determine the questions offered and so is safely ignored.
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