Kathy Dopp wrote:
Jonathan,
Monotonicity is a mathematical concept that is fairly simple to
describe. There is non-decreasing monotonicity, strictly increasing
monotonicity, non-increasing monotonicity, etc. Arrow describes the
concept re. elections fairly well in one of his fairness conditions.
IRV/STV are the only alternative voting methods I am aware of that
fail this monotonicity condition that Arrow's fairness condition
requires but I have not studied all alternative methods so there must
be others that fail Arrow's monotonicity criteria. Plurality
elections do *not* fail this criteria which is why IRV/STV fail more
of Arrow's fairness criteria than plurality does.
The simplest way to state it in English is that the act of voting in
any one election should be monotonically increasing by giving the
voter the right to know that voting for a candidate always increases
that candidate's chances of winning holding all other things constant
(given the votes of other voters). In other words, mathematically,
increasing the input or x value, always increases the output or y
value in a monotonically increasing function.
That could be interpreted in two ways. Do you mean that a voter adding a
ballot that ranks A above B should not cause A to lose to B, or that if
a ballot were replaced by one where A is moved further towards top rank,
A shouldn't lose? Or both?
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