...
1) ... I am aware that you have the final score set up as the difference between perfect and the result of the voter. However how do you define perfect utility? In your code, what did you use as the variables for utility/scores? What did you consider to be a "positive" utility factor, or a "negative" utility factor?
200 voters, 1 issue, 99 ignorance:
10 | 1.14353 1.73402 2.11705 2.40098
11 | 1.14353 1.73841 2.12829 2.42353
12 | 1.14323 1.79825 2.22756 2.52766
13 | 1.30423 1.95194 2.37133 2.67611
14 | 1.31709 1.97563 2.39908 2.71050
15 | 2.63451 3.95035 4.79655 5.41547
16 | 1.14353 1.69885 2.06326 2.33086
17 | 1.14353 1.72265 2.08869 2.36298
200 voters, 2 issues, 99 ignorance
10 | 0.88038 1.32844 1.63188 1.84345
11 | 0.88038 1.33585 1.63582 1.84912
12 | 0.87997 1.36885 1.68600 1.91402
13 | 0.96744 1.45804 1.76898 1.99551
14 | 0.97695 1.47021 1.78572 2.01165
15 | 1.95559 2.93559 3.57001 4.02250
16 | 0.88038 1.30893 1.59450 1.80465
17 | 0.88038 1.32445 1.60826 1.81970
200 voters, 4 issues, 99 ignorance
10 | 1.62043 3.12970 4.45909 5.57267
11 | 1.62043 3.25451 4.70978 5.97823
12 | 1.62330 5.61193 8.21399 10.06463
13 | 7.41816 11.10125 13.50752 15.28285
14 | 7.97718 11.94536 14.52958 16.42629
15 | 15.94065 23.92663 29.11791 32.86929
16 | 1.62043 1.84531 2.38968 2.83686
17 | 1.62043 2.64512 3.36122 3.8901016 | 1.62043 1.84531 2.38968 2.83686
17 | 1.62043 2.64512 3.36122 3.89010
18 | 1.62043 2.64512 3.34779 3.88619
26 | 1.62043 8.79597 11.38676 13.24482
So my question is this, if the data is trending downwards regularly and without exception, and all the points as you move from 1, to 2, to 3 to 4 are close to one another (within 1 standard deviation), why did you choose to include "infinite issues" when that data point clearly bucks the trend of the others, and suddenly we have points so far away from the mean of the previous points that it is almost 10 SD away? In statistics the 68, 95, 99 rule states that 99% of the data with normal distribution should lie within 3 SD from mean. Anything outside of this is considered to be an outlier data point and is ignored. Yet you opted to include this in your results.
I'm curious as to your reason for this choice as it clearly and dramatically affects the outcome of your test.
Part 2 - on a related note, range voting does something very odd when you move from any integer (n : N is an element of the Reals), to n being infinite. Range voting's score increases slightly as you proceed from two candidates, to three, to four regardless of the value of n so long as n is an element of the reals. But when you switch to n being infinite, the range voting score decreases from candidates moving from 2, to 3, to 4, to 5.
Examples:
Issue Based Utilities (4 Issues). IgnoranceQ=0.99. (Identical.) 200 voters.
system|2 canddts 3 canddts 4 canddts 5 canddts
------+--------- --------- --------- ---------
0 | 0.64469 0.95884 1.16057 1.30883
Random-Normal(0,1) Utilities (infinite issue limit). IgnoranceQ=0.99. (Identical.) 200 voters.
system|2 canddts 3 canddts 4 canddts 5 canddts
------+--------- --------- --------- ---------
0 | 1.62043 1.36920 1.17042 1.03423
You opted to include this data in every one of your examples, and in your results yet the general trend of the data is completely the reverse of the previous established pattern. With any numerical value of issues where n = element of reals, range voting's score increases. With infinite issues, it suddenly reverses and decreases.
My question for part 2 is the same as part one. Clearly your data is altered, not just in scope, but in direction and orientation as well. Thus the infinite data point isn't useful in measuring against the other numerical data points. Based on this data, my best guess for the mathematical function of your program is that it behaves in some fashion like the graph Y = (X^3)((X-5)^4)+3 in so much as it gives good data within a small domain (2<X<5) but after this point it increases exponentially and in the opposite direction to the trend. Most mathematicians and statisticians know not to use data from this end point as it is a statistical outlier and will drastically skew their results. You opted to keep it in. I'm curious as to your reasoning for this decision.
RE: topic #1 - Thank you for the links but I'm afraid they did not answer my question. They did however provide me with an example I can show you to illustrate my question. You wrote, "The sum over all voters V of their utility for X, maximized over all candidates X, is the "optimum societal utility" which would have been achieved if the election system had magically chosen the societally best candidate. "
(ii) a decreasing ordering, supplied by "God" of the presumed likelihoods
each candidate will win.
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On Jan 12, 2017 11:37 AM, "Jameson Quinn" <jameso...@gmail.com> wrote:
>
> https://github.com/The-Center-for-Election-Science/vse-sim
>
By the way, https://github.com/electology is a thing. Jameson, if you want access, I would be more than happy to provide it.
Best,
Leon
> 2017-01-12 11:20 GMT-05:00 William Waugh <2knuw...@snkmail.com>:
>>
>> Are you publishing the source code?
>>
>> On Thursday, January 12, 2017 at 7:32:06 AM UTC-5, Jameson Quinn wrote:
>>>
>>> https://groups.google.com/d/msg/electionscience/do8-1wQLXB4/uMPksH8qAQAJ
>>
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You all are the CS people so I will ask you.