[EM] How choice of voting systems depend on amount of participants

[Richard Fobes]

On 9/29/2014 9:10 PM, dikov dikov wrote:
 >  >The number of _choices_ (candidates) does make a big difference on the
 >  >results. In contrast, the number of _voters_ does not make a big
 >  >difference (except that ties are more likely if there are a small 
number
 >  >of voters).
 >
 > So if a contest assumes only one winner than any method is valid, right?

"Any method is valid" is not what I was trying to say.  Those of us in 
this forum have different opinions about which voting method is "valid."

Getting back to what I think you originally asked, when a specific 
voting method has been chosen, the difference between lots of voters and 
a few voters does not matter -- in the mathematical sense.

(As Kristofer pointed out, a small number of voters does make it easier 
for the voters to communicate among themselves for strategy purposes.)

So, to be clear, if you choose voting method A, the number of voters 
does not cause counting problems if there are lots of voters instead of 
a few voters.  (This statement applies regardless of which voting method 
A you choose -- except for the case of instant-runoff voting when there 
are districts involved.)

But, if you also consider voting method B, and compare it to voting 
method A, that is a very different issue.  It's very complicated, and it 
is the primary topic discussed in this forum.

Richard


On 9/29/2014 9:10 PM, dikov dikov wrote:
> Thank you a lot for explanation Richard.
>
>
>  >The number of _choices_ (candidates) does make a big difference on the
>  >results. In contrast, the number of _voters_ does not make a big
>  >difference (except that ties are more likely if there are a small number
>  >of voters).
>
> So if a contest assumes only one winner than any method is valid, right?
>
>
> Dmytro
>
>
>
>
> On Thursday, September 25, 2014 11:42 AM, Richard Fobes
> <ElectionMethods at VoteFair.org> wrote:
>
>
> On 9/25/2014 7:46 AM, dikov dikov wrote:
>  > Basically, I had an idea that upon setting a contest, one would have a
>  > pull down menu with voting systems accompained with comments explaining
>  > under which circumstances what system would give better results.
>
> Describing which voting method has which characteristics is very
> challenging. To see why, look at this table in Wikipedia:
>
>
> http://en.wikipedia.org/wiki/Voting_system#Compliance_of_selected_systems_.28table.29
>
> Typically when there is a choice of voting method, there is a table that
> shows who the winner is for each of the voting methods. This is what's
> done at VoteFair.org.
>
>  > I exactly assumed that for small polls (say 10 voters) a simple majority
>  > with only one winner can be more favorable than scoring all entries in
>  > ballots.
>
> I don't understand what you mean here.
>
> A simple majority is only assured if there are just two
> candidates/choices. (Except in the case of a tie.)
>
> If one of the candidates/choices gets a majority (more than half the
> votes), then all the "good" voting methods would declare that
> candidate/choice as the winner. This means the choice of voting method
> does not matter if there is a majority winner.
>
> The number of _choices_ (candidates) does make a big difference on the
> results. In contrast, the number of _voters_ does not make a big
> difference (except that ties are more likely if there are a small number
> of voters).
>
> Richard Fobes