[gwnn]

There's a chess tournament and they have several special prizes (in $$$).

There are also some prizes for the best overall players but those are not interesting for this question.

There's a prize for best under 1800 ranking and one for best under 1600.

Suppose you want to respect the following (reasonable) principles when deciding who gets them:

1. If you are eligible for more than one prize, you get the highest one, but only one.
2. If more than one people are eligible for a prize and they finished with the same points, there is no tiebreak, they get to split the prize.

Suppose there are five people in a tiebreak (places 16-20 out of 100 players) with the rankings
1740
1680
1550
1500
1390.

All of the players finishing above these five have more than 1800 ELO so they will definitely not get any money out of these two prizes. The two special prizes have the same amount: 100$.

Who gets what???

[Aberlour10]

1740 $50,00
1680 $50,00
1550 $33,33
1500 $33,33
1390 §33,33

it seems logic to me this way...

[BunnyGo]

It seems to me that the players under 1600 should get at least as much money as those between 1600 and 1800 (they should be penalized for having a lower ranking?) With this in mind, there seem a few reasonable ways of dividing up the money:

1) All of them divide up the 1800 prize money, and someone else gets the 1600 prize money.

2) All of them divide up the 1800 prize money, and the three under 1600 also divide up the 1600 prize money.

3) All 5 people get $40.

I think that Aberlour10's suggestion unfairly penalizes the players with ranking below 1600--they were eligible for both prizes, and should get the maximum award, not the minimum.

[Aberlour10]

I see your arguments... but its the matter of interpretation of point 1. posted by gwnn

"1. If you are eligible for more than one prize, you get the highest one, but only one

The 3 players under 1600 are eligible for 2 prizes, if they would get one for U1800 they would get 100/5 = 20$ each and it is not the highest one, because getting one prize for U1600 they would earn more = $33,33 each
This is my interpretation of point 1.

[BunnyGo]

Aberlour10, on 2011-January-03, 18:30, said:

I see your arguments... but its the matter of interpretation of point 1. posted by gwnn

"1. If you are eligible for more than one prize, you get the highest one, but only one

The 3 players under 1600 are eligible for 2 prizes, if they would get one for U1800 they would get 100/5 = 20$ each and it is not the highest one, because getting one prize for U1600 they would earn more = $33,33 each
This is my interpretation of point 1.

Agreed, but my option (3) can be viewed as filling this option. The two 1800 people are assigned the 1800 prize. The first two 1600 players will make more by getting the 1600 prize, but then the last person gets the most by taking "1/2 of each".

This works better with 6 people (2 in 1800, 4 in 1600). Say that we do your assignment. Then the 4th 1600 player would actually do best by getting the 1800 prize. But this has a disappointing lack of symmetry.

[nigel_k]

Split the under 1800 prize five ways and the under 1600 prize three ways. So the under 1600 people get a share of both.

Condition 1 is inherently unfair so it shouldn't be surprising we can't stick to it precisely and still come up with something that seems intuitively fair. I would get around it by just saying that nobody is getting more than one prize. The most people are getting is one third of one prize and one fifth of another.

[awm]

I'd suggest that condition (1) means no player can get more than one total prize. So here we have:

The 1800 prize is shared 5 ways ($20 to all) and the 1600 prize is shared three ways ($33). So:

1740: $20
1680: $20
1550: $53
1500: $53
1390: $53

Note that no player received more money than the maximum prize he was in the tiebreak for (which was $100). If we had only two people in the tiebreak say 1740 and 1550, then the person with 1550 is eligible for half the 1800 prize ($50) and all the 1600 prize ($100) but he can't receive more than $100 (the value of the largest prize he is eligible for) and thus receives $100 only. This leaves 1740 getting $100 also.

[JLOGIC]

I thought the same ratio as adam

[Fluffy]

also the same as adam, I can see that being picky with the 2 prices rule might mess this sharing, but it is the (most fair, I think fairest doesn't exist) way to do it.

[Aberlour10]

I am not altogether convinced. Surely this seems to be the fairest solution, but the question is not... what is fairest way but rather what the conditions of the contest allowing. IMO there is a violation of §1)... There would be no problems if the §2) would say...
"2. If more than one people are eligible for the prizes and they finished with the same points, there is no tiebreak, they get to split the prizes.

But it doesn't say this..

[gwnn]

Just to clarify, this is not copied from a lawbook, it's just my little words obviously
1) refers to a situation where there is only one person who is eligible for more than one prize and
2) refers to a situation where there is only one prize and there's more than one person eligible for it

The principles are real (from a real tournament), and I did not ask for clarification from anyone and this situation never occurred.

It almost occurred with 1 under 1800 and three under 1600's.

[hrothgar]

gwnn, on 2011-January-03, 17:18, said:

Suppose you want to respect the following (reasonable) principles when deciding who gets them:

1. If you are eligible for more than one prize, you get the highest one, but only one.
2. If more than one people are eligible for a prize and they finished with the same points, there is no tiebreak, they get to split the prize.

If I wanted to respect said principles, then:

The players with ratings under 1,600 are eligible for both the under 1800 prize and the under 1600 prize.
These players therefore share in the pool for the under 1800 prize.
This, in turn, cancels their eligibility for the under 1,600 prize

The players with a rating over 1,600 but under 1,800 are eligible for the under 1,800 prize only.

1. Therefore, the under 1,800 prize gets split 5 ways (each player gets $20)
2. None of these players is elible for the under 1,600 prize which gets awarded to someone else

FWIW, I don't think that I'd want to respect said principles...

[VMars]

If using the principles of how masterpoints are awarded in ACBL (which seem to follow rule 1), I would award:

1740: $20
1680: $20
1550: $33
1500: $33
1390: $33

The prize for under 1800 was split between five, so each would be eligible for $20, and the prize for under 1600 was split between three, so each would be eligible for $33, and since $33 is greater than $20, they get the $20. If we don't like that we don't distribute all of the prizes, then I would use awm's suggestion.

[JLOGIC]

VMars, on 2011-January-04, 17:35, said:

If using the principles of how masterpoints are awarded in ACBL (which seem to follow rule 1), I would award:

1740: $20
1680: $20
1550: $33
1500: $33
1390: $33

The prize for under 1800 was split between five, so each would be eligible for $20, and the prize for under 1600 was split between three, so each would be eligible for $33, and since $33 is greater than $20, they get the $20. If we don't like that we don't distribute all of the prizes, then I would use awm's suggestion.

Veronica Mars was a great show

[cloa513]

VMars, on 2011-January-04, 17:35, said:

If using the principles of how masterpoints are awarded in ACBL (which seem to follow rule 1), I would award:

1740: $20
1680: $20
1550: $33
1500: $33
1390: $33

The prize for under 1800 was split between five, so each would be eligible for $20, and the prize for under 1600 was split between three, so each would be eligible for $33, and since $33 is greater than $20, they get the $20. If we don't like that we don't distribute all of the prizes, then I would use awm's suggestion.

Logically
Basically it splits the tie into two ties- one for the top prize and one for the bottom.
1740: $50
1680: $50
1550: $33
1500: $33
1390: $33

[Elianna]

gwnn, on 2011-January-03, 17:18, said:

There's a chess tournament and they have several special prizes (in $$$).

There are also some prizes for the best overall players but those are not interesting for this question.

There's a prize for best under 1800 ranking and one for best under 1600.

Suppose you want to respect the following (reasonable) principles when deciding who gets them:

1. If you are eligible for more than one prize, you get the highest one, but only one.
2. If more than one people are eligible for a prize and they finished with the same points, there is no tiebreak, they get to split the prize.

Suppose there are five people in a tiebreak (places 16-20 out of 100 players) with the rankings
1740
1680
1550
1500
1390.

All of the players finishing above these five have more than 1800 ELO so they will definitely not get any money out of these two prizes. The two special prizes have the same amount: 100$.

Who gets what???

Let's say that place 16 was won straight out by someone with a 1390, and place 17 was won straight out with a 1740. (All others ahead were above 1800.) Does this mean that the committee would award two prizes, one each to the 16th placer and 17th placer, or award a prize ($100) to the 16th placer and then not to the 17th placer? I would guess the latter, and if so, then clearly $20,$20,$33,$33,$33 is the correct way to split. If the former is what would happen (and how would that fit in the rules) then I don't know which would fit, but Adam's response seems equitable.

And I agree with Justin.

And don't understand how cloa's point is at all related to the portion (s)he quoted.

[gwnn]

Yes the organisers said that actually the under 1800 prize is 100$ and 10 cents, to clear up confusion over Elianna's case (but I never got the 10 cents).