http://dylanleigh.net/enThu, 08 Jan 2026 15:46:12 GMTNikola (getnikola.com)http://blogs.law.harvard.edu/tech/rsshttp://dylanleigh.net/posts/2019/12/non-monotonicity-in-australian-preference-voting/Dylan Leigh<div><p>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).</p> <p>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.</p> <p>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.</p> <p><a href="http://dylanleigh.net/posts/2019/12/non-monotonicity-in-australian-preference-voting/">Read more…</a> (4 min remaining to read)</p></div>australiacombinatoricsmathematicspoliticshttp://dylanleigh.net/posts/2019/12/non-monotonicity-in-australian-preference-voting/Wed, 18 Dec 2019 01:14:48 GMThttp://dylanleigh.net/posts/2019/11/sunday-maths-the-diagonal-sum-mental-multiplication-method/Dylan Leigh<div><p>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.</p> <p>It converts an n × n multiplication problem into a n² set of single digit multiplications, arithmetically identical to the <a class="reference external" href="http://mathworld.wolfram.com/LatticeMethod.html">"Lattice Method"</a>. 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.</p> <p><a href="http://dylanleigh.net/posts/2019/11/sunday-maths-the-diagonal-sum-mental-multiplication-method/">Read more…</a> (4 min remaining to read)</p></div>algebraarithmeticcombinatoricsmathematicsmental mathsciencehttp://dylanleigh.net/posts/2019/11/sunday-maths-the-diagonal-sum-mental-multiplication-method/Sun, 24 Nov 2019 05:34:18 GMThttp://dylanleigh.net/posts/2019/11/sunday-maths-quickly-multiplying-teens/Dylan Leigh<div><p>In a similar vein to <a class="reference external" href="http://dylanleigh.net/posts/2019/11/sunday-maths-simplifying-squares/">last week's post on simplifying squares</a>, this one uses some basic algebra to make it easier to multiply numbers between 10-20:</p> <pre class="literal-block">(10 + x)(10 + y) = 100 + 10x + 10y + xy = 10(x + y + 10) + xy</pre> <p><a href="http://dylanleigh.net/posts/2019/11/sunday-maths-quickly-multiplying-teens/">Read more…</a> (1 min remaining to read)</p></div>algebraarithmeticcombinatoricsmathematicsmental mathsciencehttp://dylanleigh.net/posts/2019/11/sunday-maths-quickly-multiplying-teens/Sat, 09 Nov 2019 14:47:05 GMThttp://dylanleigh.net/posts/2019/11/sunday-maths-simplifying-squares/Dylan Leigh<div><p>This is a simple method to make it easier to calculate squares in your head (or on paper). The key is the following equation:</p> <pre class="literal-block">x² = (x+y)(x-y) + y²</pre> <p><a href="http://dylanleigh.net/posts/2019/11/sunday-maths-simplifying-squares/">Read more…</a> (1 min remaining to read)</p></div>algebraarithmeticcombinatoricsmathematicsmental mathsciencehttp://dylanleigh.net/posts/2019/11/sunday-maths-simplifying-squares/Sun, 03 Nov 2019 04:49:23 GMT