There are several methods of voting which allow voters to rank candidates in order of their preference, rather than just selecting a single desired candidate and then doing a single count (Plurality or “First Past the Post” voting). The system specifically used in Australian elections is “Instant-Runoff Voting” (IRV).

IRV is intended to allow for a variety of political parties of various sizes to flourish (unlike the famously two-party-dominated politics of the USA) as citizens who vote for a minor party as their first preference don’t “waste” their vote; if their first preference is too obscure to get in, their vote goes to their second preference, and so on.

However, it is still possible for “vote-splitting” to have a negative effect on minor parties - in some cases, giving a candidate a higher preference can paradoxically cause them to lose, as they can be eliminated earlier.

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This is a mental math technique to solve non-trivial integer multiplication I picked up from one of Arthur Benjamin’s talks, and is widely used by other “mathemagicians” to solve large products.

It converts an n × n multiplication problem into a n² set of single digit multiplications, arithmetically identical to the “Lattice Method”. However, instead of filling the lattice first and then summing each diagonal, this method calculates each sum as soon as possible - thus you only need to keep track of the bare minimum of working data and it becomes possible to do the problem entirely in your head.

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In a similar vein to last week’s post on simplifying squares, this one uses some basic algebra to make it easier to multiply numbers between 10-20:

(10 + x)(10 + y) = 100 + 10x + 10y + xy = 10(x + y + 10) + xy

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This is a simple method to make it easier to calculate squares in your head (or on paper). The key is the following equation:

x² = (x+y)(x-y) + y²

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