The EU Browser Ballot and Random Sorting

2718.us — Wed, 24 Feb 2010 02:09:44 +0000

An Ars Technica “etc” post linked to a TechCrunch article (apparently based on a Slovakian article, but I didn’t look into the Slovakian article to be sure) that talks about the ordering of the browsers in Microsoft’s EU Browser Ballot not being uniformly distributed. At a glance at the Javascript that does the randomizing of the browsers (randomly orders the top 5, and randomly orders the rest), it appears to randomize by calling the Javascript array sort with a comparison function that returns < half the time and > the other half of the time. I believe that this is likely the underlying cause of the non-uniformity of the orderings.

The second result in a google search for “javascript sort” says:

To randomize the order of the elements within an array, what we need is the body of our sortfunction to return a number that is randomly <0, 0, or >0, irrespective to the relationship between “a” and “b”. The below will do the trick:
//Randomize the order of the array:
var myarray=[25, 8, "George", "John"]
myarray.sort(function() {return 0.5 - Math.random()}) //Array elements now scrambled

This is almost exactly the method of randomization used in the browser ballot javascript.

To test the results of this randomization technique, I applied it 1,000,000 times to the list {0,1,2,3,4} in Mathematica and tabulated the relative frequencies of each number in each position. (Rounded to the nearest whole %).

position/number	0	1	2	3	4
first	18%	12%	12%	12%	47%
second	18%	24%	18%	18%	24%
third	20%	21%	27%	20%	12%
fourth	22%	22%	22%	28%	6%
fifth	22%	22%	22%	22%	12%

At a glance, it appears that the distribution is far from uniform. My quick attempt at re-learning how to use the Χ² test gave a probability less than 1×10^-100000 that this data matched a uniform distribution (if someone can confirm/fix that, please comment).

I used the Mathematica Sort[] command to do the sorting. I don’t know what algorithm that uses. It appears that the algorithm used by Javascript’s sort() varies from browser to browser, though the browser ballot would be displayed in IE8 by default. I suspect that the distribution is highly dependent on the sorting algorithm used, though I cannot readily verify it [edit: I verified it]. Regardless, this seems to be a very poor way to generate a random ordering.

js, jQuery, and AJAX

2718.us — Sun, 06 Apr 2008 23:07:29 +0000

Through the tail end of last week and into this weekend, I’ve been learning some (more) javascript, learning to use the jQuery library/framework, and learning to make AJAX work. I’ve discovered just how much of a royal pain it is to trap keyboard events in a way that works across platforms (mac-pc, mostly, is what I care about), though I did get pretty much all of the keyboard stuff I wanted working (arrow keys, ctrl+arrow keys, enter key). I also learned how to make the page communicate back to a PHP backend via AJAX in a sensible way (buffering data to be sent back so as to prevent thrashing the server).

This is all in stark contrast to my previous experience with script.aculo.us, wherein I was able to make some really nifty shiny stuff work really well without having to learn too much, but it was still all traditional client-server and nothing properly AJAX and all the workings of the javascript were so specific to script.aculo.us that I didn’t really learn any js. jQuery seems much more straight-forward, even though it also seems to provide only a much lower level of functionality, though I did start to fiddle with animations with jQuery.

Hopefully, some jQuery and AJAX will find their way into some of my production stuff in the next few weeks.

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The EU Browser Ballot and Random Sorting

js, jQuery, and AJAX