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The PS-lottery algorithm is an improvement of PS in which the lottery is done only among deterministic allocations that are envy-free-except-one-item (EF1). This guaratees that the ex-post allocation is 'not too unfair'. Every effort is made to ensure the accuracy of the winning numbers, prize payouts and other information posted on the Pennsylvania Lottery's website. The official winning numbers are those selected in the respective drawings and recorded under the observation of an independent accounting firm. PICK 3 day drawing can be viewed on the PA Lottery website daily after 1:35 p.m. PICK 3 evening is drawn during the nightly drawing show at 6:59 p.m. Watch for the evening drawing on TV, streaming online or check PA Lottery drawing results on your local TV station. Also, please take a few moments and review the rules for posting at Lottery Post. Any time you see a gray-underlined link, you can click the link to see a popup menu of options.
The probabilistic serial procedure (PS), also called serial eating algorithm, is a procedure for fair random assignment. It yields a randomized allocation of indivisible items among several agents that is both envy-free and Pareto efficient. It was suggested by Hervé Moulin and Anna Bogomolnaia.[1]
Description[edit]
Each item is represented as a loaf of bread (or other food). Initially, each agent goes to their favourite item and starts eating it. It is possible that several agents eat the same item at the same time.
Whenever an item is fully eaten, each of the agents who ate it goes to their favorite remaining item and starts eating it in the same way, until all items are consumed.
For each item, the fraction of that item eaten by each agent is recorded. These fractions are considered as probabilities. Based on these probabilities, a lottery is done. The type of lottery depends on the problem:
- If each agent is allowed to receive any number of items, then a separate lottery can be done for each item. Each item is given to one of the agents who ate a part of it, chosen at random according to the probability distribution for that item.
- If each agent should receive exactly one item, then there must be a single lottery that picks an assignment by some probability distribution on the set of deterministic assignments. To do this, the n-by-n matrix of probabilities should be decomposed into a convex combination of permutation matrices. This can be done by the Birkhoff algorithm. It is guaranteed to find a combination in which the number of permutation matrices is at most n2-2n+2.
An important parameter to PS is the eating speed of each agent. In the simplest case, when all agents have the same entitlements, it makes sense to let all agents eat in the same speed all the time. However, when agents have different entitlements, it is possible to give the more privileged agents a higher eating speed. Moreover, it is possible to let the eating speed change with time.
Example[edit]
There are four agents and four items (denoted w,x,y,z). The preferences of the agents are:
- Alice and Bob prefer w to x to y to z.
- Chana and Dana prefer x to w to z to y.
The agents have equal rights so we apply PS with equal and uniform eating speed of 1 unit per minute.
Initially, Alice and Bob go to w and Chana and Dana go to x. Each pair eats their item simultaneously. After 1/2 minute, Alice and Bob each have 1/2 of w, while Chana and Dana each have 1/2 of x.
Then, Alice and Bob go to y (their favourite remaining item) and Chana and Dana go to z (their favourite remaining item). After 1/2 minute, Alice and Bob each have 1/2 of y and Chana and Dana each have 1/2 of z.
The matrix of probabilities is now:
Alice: 1/2 0 1/2 0
Bob : 1/2 0 1/2 0
Chana: 0 1/2 0 1/2
Dana: 0 1/2 0 1/2
Based on the eaten fractions, item w is given to either Alice or Bob with equal probability and the same is done with item y; item x is given to either Chana or Dana with equal probability and the same is done with item z. If it is required to give exactly 1 item per agent, then the matrix of probabilities is decomposed into the following two assignment matrices:
1 0 0 0 0 0 1 0
0 0 1 0 1 0 0 0
0 1 0 0 0 0 0 1
0 0 0 1 0 1 0 0
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One of these assignments is selected at random with a probability of 1/2.
Properties[edit]
Fairness[edit]
PS satisfies a fairness property called (sd-envy-free). Informally it means that each agent, considering the resulting probability matrix, weakly prefers his/her own row of probabilities to the row of any other agent. Formally, for every two agents i and j:
- Agent i has a weakly-higher probability to get his best item in row i than in row j;
- Agent i has a weakly-higher probability to get one of his two best items in row i than in row j;
- ...
- For any k ≥ 1, agent i has a weakly-higher probability to get one of his k best items in row i than in row j.
Note that sd-envy-freeness is an ex-ante fairness notion: it is fair only before the lottery takes place. The algorithm is of course not ex-post fair: after the lottery takes place, the unlucky agents may envy the lucky ones. But this is inevitable in allocation of indivisible objects.
Efficiency[edit]
PS satisfies an efficiency property called (sd-efficiency, also called: ordinal efficiency). Informally it means that, considering the resulting probability matrix, there is no other matrix that all agents weakly-sd-prefer and at least one agent strictly-sd-prefers.
Here, the ex-ante notion of sd-efficiency is stronger than the ex-post notion: sd-efficiency implies that every allocation selected by the lottery is sd-Pareto-efficient.
Strategy[edit]
PS is not a truthful mechanism: an agent who knows that his most preferred item is not wanted by any other agent, can manipulate the algorithm by eating his second-most preferred item, knowing that his best item will remain intact.
Improvements[edit]
As explained above, the allocation determined by PS is fair only ex-ante but not ex-post. Moreover, when each agent may get any number of items, the ex-post unfairness might be arbitrarily bad: it is possible that one agent will get all the items while other agents get none.
The PS-lottery algorithm is an improvement of PS in which the lottery is done only among deterministic allocations that are envy-free-except-one-item (EF1). This guaratees that the ex-post allocation is 'not too unfair'. Moreover, the EF1 guarantee holds for any cardinal utilities consistent with the ordinal ranking, i.e., it is stochastic-dominance EF1 (sd-EF1).[2]
The algorithm uses as subroutines both the PS algorithm and the Birkhoff algorithm.
See also[edit]
- Random priority - an alternative mechanism with different properties.
References[edit]
- ^Bogomolnaia, Anna; Moulin, Hervé (2001). 'A New Solution to the Random Assignment Problem'. Journal of Economic Theory. 100 (2): 295. doi:10.1006/jeth.2000.2710.
- ^Aziz, Haris (2020). 'Simultaneously Achieving Ex-ante and Ex-post Fairness'. arXiv:2004.02554 [cs.GT].
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Genshin Impact – miHoYo Gifts Employees RTX 3070 Cards, PS5 and Switch Consoles Through Lottery Prizes For Chinese New Year
If you still need proof miHoYo has struck gold with Genshin Impact (PC, PS4, PS5, Mobile, Switch soon): through a lottery for Chinese New Year celebrations, the company will gift its employees PS5 consoles, Switch consoles, iPhones, RTX 3070 graphic cards, and several pieces of hardware.
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Only initially shared on Weibo, several photos of mountains of various hardware at miHoYo’s offices have been making the rounds on Japanese anonymous messages boards today, before ending up on several Japanese matome blogs.
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China and several communities around the world will celebrate the Chinese new year on February 12, 2021 this year. Note that you can spot all miHoYo games and projects in the last picture. With the miHoYo mascots, official miHoYo VTuber YoYo Lumi, alongside characters from Honkai Impact 3rd, Genshin, and Tears of Themis.
Wasn’t that hard gathering so many consoles, considering Genshin Impact has been incredibly popular since its official launch on September 28, 2020. The game definitely deserves it seeing its overall high quality, be it its story elements or gameplay. And sure, there’s a gacha system, but it’s definitely valid to bring up the “nothing force you to pull the gacha” card in here, seeing Genshin Impact unlike 99% of games with gacha elements has ton of stuff to do regardless of Gacha or Stamina. With an open-world to explore. Moreover, the endgame content can be cleared without the need of rarer characters obtainable via Gacha. Anyways, it’s nice to see miHoYo employees are reaping the fruit of their hard work. Here’s hoping Version 1.3 will be just as awesome.
Doing a voice quite similar to Kirito from Sword Art Online, popular seiyuu Yoshitsugu Matsuoka voices Xiao, the new upcoming character of Genshin Impact. Xiao will be added with the Version 1.3 update on February 3, titled All That Glitters.
A web event for Genshin Impact titled Slime Paradise is currently ongoing. Once it ends on January 31, we go back to the usual Slime Genocide instead. As while the event requires you to take care of them, Slimes are among the most common enemies in Genshin Impact for now, and are quite annoying to boot. Hopefully we’ll get to explore more parts of the map with new enemies soon, and hopefully get Inazuma later this year. Note that starting the Slime Paradise event now is too late to get all its rewards. However, you can check all the events and artwork from Slime Paradise here. Last but not least, the list of final adjustments for Zhongli and Geo characters in Version 1.3 should be published soon by miHoYo.
The post Genshin Impact – miHoYo Gifts Employees RTX 3070 Cards, PS5 and Switch Consoles Through Lottery Prizes For Chinese New Year by Iyane Agossah appeared first on DualShockers.
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Genshin Impact – miHoYo Gifts Employees RTX 3070 Cards, PS5 and Switch Consoles Through Lottery Prizes For Chinese New Year
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