All entries for Monday 30 January 2006
January 30, 2006
… time flies like an arrow, which brings me neatly on to the theory of social choice functions (better known to most of us as 'voting systems'). Arrow's Theorem states, in a nutshell, that the only voting system that satisfies three very plausible 'fairness criteria' (for example, if more voters prefer X to Y, then X should appear above Y in the final list) is a dictatorship, where one person gets to decide for everyone else.
Could there be an analogue of Arrow's Theorem for marking objective tests? Is there a marking system that is fair to all? To answer this, one first needs a list of fairness criteria. Any suggestions for these? I'll start the ball rolling with
Criterion 1: If student X 'knows more' than student Y, then X should score more than Y. Of course, the examiner has to specify what is meant by 'knows more'.