# [EM] I need an example of Condorcet method being subjected

Sat Jan 23 04:05:42 PST 2010

```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?

```