Everyone needs to play around with this graphical voting simulator. Be sure to click on the help link at the top, so you can know what all the features do (and to find the link to two-dimensional voting simulation graphics.) At a minimum, you should click on and enable the displays for plurality, approval, and Hare (IRV), as well as enable a third candidate; then slide the candidates around. From this, it should be very easy to highlight the short-comings of plurality, and see the sorts of bizarre and non-intuitive results that IRV can give.
For instance, you should easily be able to construct a case demonstrating the non-monotonicity of IRV, which will show up as bands of a candidate's color being disjointed (for instance, red-yellow-red). Or, a case where the point directly above the candidate's marker in IRV (or plurality) is not the same color as the candidate; meaning that, even if the candidate were perfectly-centered in the voter distribution, they would not win the election. I think that is something that, with this model, cannot ever be the case for approval voting, but I'm not 100% certain of that (the non-normal distributions are probably the best bet for proving me wrong.)
You can also demonstrate the effect of "spoilers" (or, in Borda, "teaming") by toggling candidates on and off, and noting how the winner changes.
Have fun!
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