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Calculate the payout percentage for each winner if you choose to award a and divide it up based on the number of prize categories winners.


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At the end of the season, we collect the money and divide it up, with are combined and split in half, thus eliminating the 3rd place payout.


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Dividing amount unequally in tournament winners? fractions. Hi I am trying to write the algorithm to calculate the winning amount of the winners.


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Divide the money among players who tie for a position. For example, if three players tie for third place in a $5 million event, add the percentages normally awarded.


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How should prize money be divided in order to generate the most high-quality submissions to a contest? Suppose you are putting on an essay.


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Of course, your division of prize money may involve more factors than just quality of submissions. Any parts of the problem that aren't specified for example, how the probability of any single essay writer producing a good essay varies with the overall amount of prize money , are left up to you to assume, and should be stated. I would think it depends on the amount of money you have, and how much it's worth to your contestants to write an essay. I would have been more attracted to a more, but definitely not entirely, distributed prize structure. My motto is, "even if you lose, you get to eat cake! Its fucked up and unfair, but I submitted good stuff to them because that is how the rich and upperclass fuckers who work that way out-compete kids who were like me. I would agree that a substantial top prize would be best. Frankly, I don't think many people go into a contest of any sort with a lot of thought about the non-first prizes. There's no purely mathematical way to derive anything useful from your list of requirements. If the current users are risk neutral, then the consumer value-maximizing award is a single grand prize. If the objective is to target current users, then the number of prizes awarded should be lower than in the case where the targets are switchers. If you want to increase submissions using prize money as the motivator, I think you need to give potential submitters the idea that they have a decent chance at getting a payoff. How to divide prize money? I would also submit that a potentially even better way would be a prestigious panel of judges or something else that is going to motivate the better essay writers. The results of the model prescribes that the firm should begin by setting sweepstake objectives in terms of either attracting switchers or targeting current users. The top prize amount is clearly the most important factor. Offering lots and lots of smaller prizes may result in lots of entries, but I don't think you'd get more than you would with a single, large prize. I simply don't think that the prize split has all that much to do with how many good essays you're going to get. If you're looking for a formula, I'd imagine that the only way to get one would be by running a series of real-world studies. If its aimed at old and established folks just go with the irrational high first prize. Since baking a cake is no small undertaking, I have to combat the constant sense that there's no chance you could win, especially with how great some of the entries are. If the expected value of writing a good essay is greater than the costs, you'll get em in spades. Often, when the prizes are products rather than cash, the firm may obtain quantity discounts for the products but the value of the products will be the same for the sweepstake participants. Maybe not. For me, they're practicing cake baking. Another recommendation from the model analysis is that the firm should minimize the number of prizes at each level. Other factors that may influence quality are the nature of the pool of entrants for your contest, other rewards associated with the contest, such as publication or esteem within the group, and so on. If the non-loyal customers are risk averse in gain and loss averse, then the best prize allocation is to have both multiple large prizes as well as several small prizes. So gift them something and threaten to taken it away if their essay doesn't pass your criteria. I just keep coming back to this. To trade-off between the logistical and communication costs and the theoretically value-maximizing approach, firms could increase the number of prizes at each level for easier implementation. In practice, the costs of implementing and communicating such a prize structure could be high. In that situation, I would figure out how many people of the group would be considered good enough that their presence would discourage the others, and have twice that many prizes, all of equal value When I was a kid doing contests like these, I definitely saw them on an effort to rational expected gain basis. With the prize budget I was given, I decided to go with no more than 5 prize positions in each of the two categories, with a few extra prizes for "honorable mentions" and such. A second threshold might be one of 'making a supreme effort'. Thanks for the analysis everyone! A smaller prize would tend to lead to such behaviours as just tidying up an old essay or rushing something off in the hope that it stands a chance. In a case like this, I think you'd be better off with a bunch of smaller prizes so long as each prize was large enough to be worth having. Probably topic selection or if there is any topic would have a lot to do with how many bad essays people submit. In a school essay situation, I'd imagine there would be a handful of individuals that knew they were among the best writers in the school or class, and that handful of students might each try very hard to win a large top prize while everyone else participates half-heartedly if at all because they think the effort is futile. My point is, I could easily divvy up the prizes with my contest in a more egalitarian way. Then how on earth can you do things like award 1st, 2nd and 3rd place? Maybe multiple categories of top prizes? First in category X has a better ring to it than third place anyway. Divide your total prize money up into prizes of that amount. People will participate if they're interested in the concept and even more so if they look at it as a way to practice an ability. Which is where things might fall apart if those essays are arbitrarily assigned a value by your firm as people redeem their essays until you're bankrupt. I saw contests with four or five more impressive titles before "first" was listed. If the non-current user segment is risk neutral with respect to gains but sufficiently risk averse in the domain of losses, then the prescribed reward structure is to have a single grand prize but also include several small prizes which ideally should be close to the opportunity cost of the customers. So this second threshold is the one that gets you quality. But I certainly wouldn't get people putting the time and effort this year's winners put into their entries. Engaging in title inflation by doing things like awarding first places in categories will go a much longer way. There'll be a threshold at which participation becomes attractive. And I don't think the average quality would be nearly as high. Maybe a bit Machiavellian, so check you moral compass, but the general idea is that people are more motivated by losing something than gaining something. If the contestants don't know each other then a large prize might be more effective as more of them can fantasize that they are good enough to win. Do the contestants know each other and have some sense of each others' abilities? It's hard to say. Suppose you are putting on an essay contest, and your goal is to generate the most good essays as possible. After that, in something that's fairly subjective, like an essay contest, I would probably have a second tier of three places, all equal, who get a nice sum, and maybe a bottom tier of six who get the equivalent of a free lunch. The top prize needs to be worth significantly more than the value the writer would place on the time and energy it takes to write an essay. Since nearly everyone is going to lose, it makes more sense to distribute the prizes a bit more top-heavy and to make it something people really shoot for. Honorable mentions or "spirit" awards will mean as little to your more organized students as they will to their reach colleges. Cruel, manipulative and effective.{/INSERTKEYS}{/PARAGRAPH} {PARAGRAPH}{INSERTKEYS}Happy site news: today we welcome our 2 new mods travelingthyme and loup! When the firm's objective is to draw sales away from competitors, the value-maximizing strategy is to distribute the award money over more prizes. You're right to consider whether people will be thinking about anything other than the top prize when they decide to enter; my gut says it won't be part of their decision. A trade-off is involved between increasing the attractiveness of the sweepstake and the implementation costs of administering several levels of prizes. I suppose a secondary goal could be discouraging the submission of bad essays, and something like the judges, or something hifalutin' about the ceremony think WordFest in the movie Wonder Boys would do much for that. Best overall , best written in crayon , best without using the letter 'E' People might think they can get a specialty prize posted by shothotbot at AM on November 16, OK, I should be working but here is some input from professionals: The results of the model show that the sweepstakes reward structure should be based on three factors: the objectives of the firm, the risk aversion of the customers, and the level of sub-additivity of probability weighting. Take from that what you will, but I'd lean more towards top-heavy, fewer prizes, then lower-value prizes given to more places. So that's the first threshold, the one that gets you lots of entries. That's enough of a struggle. On the other hand, it'd be nice to reward all the effort for the other good quality submissions. I think what most people look at in a contest is the top prize, not the lesser prizes. I'd have been more likely to put in a meaningful submission if there were ten possible outcomes I could put on college applications than if there were three with one "first". How do you decide to split it up to maximize the number of good essays? Can you survey some people in your target audience to find out what amount of money it would take to spur people into action? It also depends on your audience. That said, it still applies if this is a contest aimed at adults to whom the title would be meaningful, like ones looking for publishers. If the objective is "more good essays", the best way to do that is to maximize the audience. But really, if you want to get a lot of essays, I suggest good old loss aversion. If the current users are risk averse, then the award should consist of multiple "large" prizes. That's still a nice score for the winner, and pretty good odds of getting a nice prize if you put some work into it is still pretty darn good, better than most contests. My gut instinct is to just pay for good essays an even split among winners , and if you want to give a recognition for best of show, go nuts. Having a second or third prize can be beneficial for other reasons - less pressure on judges to make the right choice, less antagonism between competitors, and so on. That said, I would even just consider awarding the top four. The allure of grand prize is there, and it needs to be impressive. Second, suppose there is some test to determine whether an essay is good or not, and that when you test school exam essays from the same pool of contestants, 50 pass. Any good essay is worth as much as any other good essay, and any bad essay is worth nothing. This is a simplified description of a real-world contest that I'm putting on for work and having trouble thinking about. I run a large online cake contest every year that gets about , visitors and usually around submissions. If the top prize is a really meaningful amount of money, participants will be encouraged to put a lot more thought, effort and time into the essay. You can create a lot more places of trinket prizes, for balance, and hope that people enter with an eye for "maybe I'll at least place", but I think the overall quality might suffer a bit. You are given a chunk of money to give away as a prize, and told you can divide it however you like: One big prize, many equally-sized small prizes, 1st 2nd 3rd split, and so on. Other factors that determine number of entries may be your deadline and any restrictions on the topic of the essay.