with No Comments

Post No.: 0032vote


Fluffystealthkitten says:


Democracy is not perfect but is, on balance, said to be better than all the other previously tried forms of governance. No one is saying don’t ever vote, especially when some groups have fought so hard to be enfranchised – my fuzzy gripe here is about the type of voting system many democratic states employ…


It’s arguably rational not to vote under the plurality voting system (one of the crappiest voting systems there is!) if your true preferences more closely match the effect of not voting compared to voting for one party (or candidate or referendum option) – if you only marginally favour one party over all others then it’d be better to not vote at all (i.e. by not voting, you’ll be in effect giving every party on the ballot paper an equal share of your vote and thus cancelling your own vote out) than to vote for your marginally favourite party (i.e. if you do vote for this party then in effect you’ll be giving this party a 100% share of your vote and all the other parties 0%).


Imagine if you draw a bar chart with all the nominated parties lined up on the x axis (let’s say there are 5 parties), and you have 100 points to divide amongst all these parties to indicate your true preferences between them (because you’re not a zealous follower of any particular party, you really care about simply what you think is best for your country policy-wise, and so you’ve read all their manifestos carefully and found that there are some things you like and some things you don’t like about each of them, to varying degrees – that’s what we all do before we vote right?!) and you give party A 23 points, party B 22 points, party C 16 points, party D 30 points and party E 9 points.


Under the plurality voting system (which includes the ‘first past the post’ system), you’d put a tick in party D’s box, which would effectively mean you’re giving that party 100 points and all the other parties 0 points each (because it’s a crude all-or-nothing voting system). But not voting at all would in essence mean giving each party 20 points each (100/5), which would more closely reflect your truer voting preferences compared to voting for party D.


This following bit might seem slightly technical for some but you should calculate the sum of squared deviations to find out which outcome would more closely match your preferences – this is the rational test of whether voting or not voting is best for you under this voting system. You can either calculate the sum of squared deviations or the sum of absolute deviations – then you want to choose the outcome (i.e. voting for your favourite party or not voting for any party at all) that has the smallest sum of deviations away from your true preferences. In the above example figures, the sum of absolute deviations away from not voting (i.e. effectively giving each and every party 20 points each) is 30 (i.e. 3 + 2 + 4 + 10 + 11), and the sum of absolute deviations away from voting for party D (i.e. effectively giving 100 points to party D and 0 points to each of the rest) is 140 (i.e. 23 + 22 + 16 + 70 + 9); hence not voting would be closer to one’s truer preferences). Meow!


Calculated for you, if there are only two options (e.g. a ‘yes/no’ referendum) then if you’re not 75/100 points or more in favour of one of the options then don’t vote (sum of absolute deviations equals <50. Strictly, if it equals exactly 50 then it’s neither rational nor irrational to vote because it’s smack-bang in the middle). If there are three options then if you’re not 66.7/100 points or more in favour of one of the options then don’t vote (sum of absolute deviations equals <66.7). And so on. (From my quick fluffy maths (therefore please check!), the maximum sum of absolute deviations as a proportion of the total points available to share between all possible options (y) should be 1 minus 1/x = y, where x is the number of possible options. And the minimum points required before it’s rational to vote for your favourite option as a proportion of the total points available to share between all possible options (z) should be 1 minus y/2 = z. Thus with 2 options, y = .500, and z = .750; with 3 options, y = .667, and z = .667; with 4 options, y = .750, and z = .625; with 5 options, y = .800, and z = .600; etc..)


One could legitimately argue that not voting should really be equivalent to not giving any points to any party at all (instead of an equal split of 20 points each in the above example) – in which case the sum of absolute deviations for not voting will always be 100 if there are 100 points to divide. If you think this is more applicable then simply adjust the calculations to decide whether or not to vote based on which will again produce the smallest sum of deviations away from your true preferences. With the above example figures, it would still be best not to vote (100 to not vote versus 140 for voting for party D). The range of possible sums of absolute deviations here should be between 0 (if you 100% support one party and give zero merit to every other party, which sounds a bit zealous; or I suppose if you totally refuse to assign any points to any party whatsoever because you think they all have completely zero merit, which again sounds a bit zealous) and 200 (if you assigned 100% of the points to one party but then strangely voted for another party, which could possibly be done for tactical voting reasons).


A question is whether all this matters or not if every voter’s deviations all cancel out once the votes of the entire population are aggregated? This assumes that every voter is independently-minded so that there are no systematic biases though.


So the rough message that should be spread should really be ‘don’t vote unless you’re really sure what/whom you want to vote for, and don’t vote if your favourite option is only marginally more favourable than your next favourite option’. (Not a perfect analogy because it doesn’t need to be ‘the winner takes it all otherwise no one gets anything at all’ here but it’s like being asked to choose your favourite child – unless you think one is vastly better than the rest then it’s best not to pick anyone at all! It’s better that they share equal treatment than one gets it all and the rest get nothing from you.) Don’t vote if you’re uncertain or only borderline. Hence don’t be peer-pressured to vote if voting under this system would mean selecting a choice that doesn’t more closely match your truer preferences than not voting at all.


But really, if your country uses this type of voting system – the clear advice would be to change it to almost any other type of voting system e.g. Borda count, range voting, approval voting… There are many different flavours of democracy across the world or yet-tried, and there are many different voting methods. Each have their own pros and cons and no system is completely perfect in every possible way (and sometimes we cannot avoid arbitrariness at least somewhere e.g. should results require a majority, some kind of supermajority or maybe even unanimity? Should the course of action from the result of a referendum take into account the magnitude of the result (e.g. should a 55:45 result mean a softer outcome than a 75:25 result), where possible?) but most maths experts would agree they’re just about all at least better than the plurality voting system.


The plurality voting system also allows tactical voting, gerrymandering, wasted votes and spoiler candidates (which I might go into with more detail in a future post). Democratic voting is at its most crude form under this system, and with any close results in particular, the results of previous polls could’ve been very different had people’s true preferences been better captured via a better voting system (but I’m going to remain apolitical here except in general or universal terms – I won’t fart on about any current affairs (‘fart’ has other synonyms in the British language. Ahem)).


In countries like the UK and USA, the plurality voting system is so ingrained but that shouldn’t make it sacrosanct; and it is arguably broke so let’s fix it, rather than ‘it’s not broke so why fix it?’ Well even if we think things aren’t broke, they can still be improved – people frequently move house not because their existing house needs to be crumbling first. The electorate needs to be better educated though and not just stick with the simplest voting method because that’s all they can comprehend. If democracy is to be allowed to evolve, grow and improve, then it must be allowed to be questioned and challenged rather than held like something that is sacred. Question the state, whether it should even exist, and how the political structures should operate if so. Besides, what sort of authoritarian state says that one cannot freely question democracy(?!)


If your country uses this system then I’d personally recommend thinking about changing it to something more sophisticated. (We did try in the UK for an ‘alternative vote’ system (an instant runoff or ranked choice method) but this 2011 referendum result was for a no change. This proposed system was not perfect either but would’ve been better – I just don’t think enough people understood it though, but arguably one of the duties of a citizen in a democracy is to get clued up. With great power comes great responsibility!)


Meow. Again, if you’re quite clearly sure of what/whom you want to vote for then do absolutely get out there and vote! The main point of this post is that it’s not just our duty to vote – it’s our duty to get interested in and educated in political matters, then vote… plus participate in all of the other activities involved in a democracy too because democracy isn’t just about doing something once every four, five or so years.


Comment on this post by replying to this tweet:




Share this post