Refutation of the moral arguments against ever voting
Some anarchists argue in opposition to voting because violence is used to enforce laws fabricated into existence through voting, but this argument is problematic because voting can also be used to prevent laws from being fabricated.
If the elections were not rigged and there was a vote on whether or not to kill all humans. I would vote not to kill all humans. Imagine if the proposition to kill all humans passed by 1 vote because you did not vote.
Some might argue that you still should not vote because they do not believe in the legitimacy of the voting process and do not believe people have a moral obligation to follow policies just because people voted to enact policies. The fundamental problem with this argument however is that other people are under undue influence to compromise their moral principles based on the outcome of a vote even if the voting system is illegitimate and is merely a methodology of undue influence. This means that someone under undue influence to use violence to enforce the outcomes of voting may refrain from violence if your vote changes the outcome even if you are unable to persuade them of the moral illegitimacy of determining your behaviour in matters of using violence by the outcome of the voting process.
However if you will not get arrested it maybe more effective in some cases to hold up signs saying laws voted into existence are enforced through violence near voting booths than to actually vote, in other situations this may not be the case. In some cases doing both maybe possible but in other cases doing both maybe problematic.
Although I do not find these arguments against voting to be valid in all cases there maybe some cases where they are valid arguments if for example refraining from voting can influence people to disbelieve in the voting system.
The theoretical probability of voting making a difference
Your vote can never change a loss to a victory but can only effect tie breakers at best.
It takes a minimum of two votes to change a loss to a victory because it takes a minimum of one vote to change a loss to a stalemate and an additional vote to change a stalemate to a victory. It may take more than two votes if the difference in votes between the two options was more than one vote.
The probability that your vote will make a difference in an election in which there are only two options other than a stalemate. Where securing exactly 50% of the votes results in a stalemate and exceeding 50% of the votes or going below 50% of the votes results in the other two options is as follows.
Let k equal the number of voters excluding you who vote the only way you want out of the two possible choices
And therefore k+1 equals the number of voters including you who vote the only way you want out of those two possible choices if you vote
And let n equal the number of voters excluding you who vote
And therefore n + 1 equals the number of voters including you if you vote
p is the probability that a single random individual out of the other voters would have voted the way you would prefer out of the only two options and is assumed to be an independent probability
However if you do vote the probability that you vote for your preference of the only two choices is assumed to be 100% and not necessarily the value p
If you vote the probability of creating a stalemate through your single vote is equal to the probability that
k + 1 = (n+1)/2
Which would make
k = (n-1)/2
And also n = 2k + 1
If k is off from this number by a quantity as small as one vote or even one half a vote (half of a odd number is a fraction) then your vote would not create a stalemate
The probability that refraining from voting would change a stalemate to a loss in your disfavor is equal to the probability that voting would change a loss in your disfavor into a stalemate
If you do vote the probability that voting would change a stalemate into a victory in your favor is equal to the probability that
k = n/2
Which would make n = 2k
If k is off from this number by a quantity as small as one vote or even one half a vote (half of a odd number is a fraction) then your vote would not change a stalemate into a victory.
The probability that refraining from voting would change a victory into a stalemate is equal to the probability that voting would change a stalemate into a victory
The probability that voting would change a loss into a victory is equal to the probability that
k < (n/2)
And
k+1 > (n+1)/2
For example
If n = 5 and k = 2
Then
2 < 2.5 = 5/2
But
2 + 1 = 3 which is not greater than 3 = (5+1)/2
If n = 5 and k = 3 then there already is a victory and voting can not change a loss into a victory
So if 5 other people voted your additional vote could never ever change a loss into a victory as you can see if you try all possible natural number values of k
But what if 6 people voted
2 < 3 = 6/2
But
2 + 1 = 3 is not greater than 3 = 6/2
But if n = 6 and k = 3 you can change a stalemate to a victory but not a loss into a victory
And if n = 6 and k = 4 there already is a victory so you can not change a loss into a victory
To calculate the probability use the method (x = X) at the webpage below for calculating probability as this is a discrete probability function not a continuous function and only uses a single value of x not a range as exceeding the voting requirements by multiple votes will not change the outcome. Input the two values of k solved for above and add the probabilities to get the likelihood that your vote can change from a loss to a stalemate or a stalemate to a victory or do not add them and only select the appropriate single value of k if you are only interested in one of those cases. The lowercase letter x is equivalent to k here. You can also use the formulas in Wikipedia below remember to calculate the probabilities for the single discrete values which will give a very low value and not to use the probabilities for at least a certain number or less than a certain number of votes which would give incorrect answers that are highly inflated.
When plugging factorial into the equations.
Keep in mind 100! Is equal to 9.332622e+157
According to a Google search I just did which I do not know the accuracy of.
This means the numbers in both the numerator and denominator maybe so
large that it is difficult to know if you calculated them correctly even with a
computer due to how they often default to deal with numbers containing
a smaller number of digits.
The numbers used to calculate how unlikely these probabilities are are so large you may have difficulty calculating them.
https://homepage.divms.uiowa.edu/~mbognar/applets/bin.html
http://web.archive.org/web/20180518125852/https://homepage.divms.uiowa.edu/~mbognar/applets/bin.html
https://en.m.wikipedia.org/wiki/Binomial_distribution
http://web.archive.org/web/20180518130449/https://en.m.wikipedia.org/wiki/Binomial_distribution
Probability of being struck by lightning
http://web.archive.org/web/20180518145627/http://www.actualanalysis.com/llp.htm
https://citp.princeton.edu/research/voting/
https://web.archive.org/web/20180802044230/https://citp.princeton.edu/research/voting/
https://web.archive.org/web/20170825144915/https://s3.amazonaws.com/citpsite/publications/ts06full.pdf
https://web.archive.org/web/20170813132353/https://s3.amazonaws.com/citpsite/publications/ts06EVT.pdf
https://attackthesystem.com/2018/07/18/they-interfered-in-our-election-power-elite-crybabies/
https://web.archive.org/web/20180812224225/https://attackthesystem.com/2018/07/18/they-interfered-in-our-election-power-elite-crybabies/
"Man-in-the-Middle" Remote Attack on Diebold Touch-screen Voting Machine by Argonne National Lab
https://m.youtube.com/watch?v=DMw2dn6K1oI
https://web.archive.org/web/20180802035639/https://m.youtube.com/watch?v=DMw2dn6K1oI
FOX News Exposes Princeton / Diebold Vote-Reversal Story
https://m.youtube.com/watch?v=8JESZiLpBLE
https://web.archive.org/web/20180802031218/https://m.youtube.com/watch?v=8JESZiLpBLE
Princeton University Exposes Diebold voting machine flaws
https://m.youtube.com/watch?v=qtARzh4RSW8
https://web.archive.org/web/20180802031127/https://m.youtube.com/watch?v=qtARzh4RSW8
Electronic Voting Machine hacked by Computer Scientists (AccuVote-TS)
https://m.youtube.com/watch?v=rYnUksWt5HQ
http://web.archive.org/web/20161224081652/https://www.youtube.com/watch?v=rYnUksWt5HQ&app=desktop
http://web.archive.org/web/20180802041824/https://m.youtube.com/watch?v=rYnUksWt5HQ
A Hacker Shows Us How Easy it is To Manipulate Voting Machines
https://m.youtube.com/watch?v=hvOKWeW_Fog
https://web.archive.org/web/20180802042919/https://m.youtube.com/watch?v=hvOKWeW_Fog
(why I) Don't Vote
https://m.youtube.com/watch?v=xqCMJhDCdMs
https://web.archive.org/web/20181119071755/https://m.youtube.com/watch?v=xqCMJhDCdMs
The Media's Presidential Election Night Hoax - 1 of 4
vaticancatholic.com
https://m.youtube.com/watch?v=nflPhNdhSXY&list=PLE4B7F2C0CA48B936&index=2&t=0s
http://web.archive.org/web/20200502054552/https://m.youtube.com/watch?v=nflPhNdhSXY&list=PLE4B7F2C0CA48B936&index=2&t=0s
This Hoax Affects Everyone
vaticancatholic.com
https://m.youtube.com/watch?v=OynCgwmD-HM
http://web.archive.org/web/20200502055108/https://m.youtube.com/watch?v=OynCgwmD-HM
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