1 00:00:00,000 --> 00:00:02,919 hi folks its Matt again and we're going 嗨，大家好，Matt，我们要去 2 00:00:03,120 --> 00:00:04,629 to talk now about dominant strategy 现在谈论主导策略 3 00:00:04,830 --> 00:00:07,269 implementation so the idea that we're 实施，所以我们 4 00:00:07,469 --> 00:00:09,339 looking at is we have a society we have 看着我们有一个社会 5 00:00:09,539 --> 00:00:11,649 to make a decision and we're trying to 做出决定，我们正在努力 6 00:00:11,849 --> 00:00:14,769 design a mechanism that is going to take 设计需要采取的机制 7 00:00:14,968 --> 00:00:16,539 people's preferences and give us 人们的喜好并给我们 8 00:00:16,739 --> 00:00:19,659 outcomes and in particular let's start 结果，特别是让我们开始 9 00:00:19,859 --> 00:00:21,669 by looking at a situation where we've 通过观察我们已经 10 00:00:21,868 --> 00:00:24,579 got a full set of alternatives and any 有全套的替代品和任何 11 00:00:24,778 --> 00:00:26,859 possible ranking over those things so 可能对这些东西进行排名 12 00:00:27,059 --> 00:00:28,300 for instance we have a set of candidates 例如我们有一组候选人 13 00:00:28,500 --> 00:00:30,550 that we need to pick from say four or 我们需要从说四或 14 00:00:30,750 --> 00:00:33,909 five six candidates okay so we think 五六个候选人好吧，我们认为 15 00:00:34,109 --> 00:00:35,649 about the voting rules that we looked at 关于我们看过的投票规则 16 00:00:35,850 --> 00:00:38,529 earlier now we've got to make a choice 现在早些时候，我们必须做出选择 17 00:00:38,729 --> 00:00:40,299 over these candidates and in particular 这些候选人，尤其是 18 00:00:40,500 --> 00:00:42,820 what we'd like is when we ask people 我们想要的是当我们问别人时 19 00:00:43,020 --> 00:00:46,209 that they have no difficulties in 他们没有困难 20 00:00:46,409 --> 00:00:47,529 deciding what they should announce they 决定他们应该宣布什么 21 00:00:47,729 --> 00:00:49,209 should just be truthful okay so we want 应该是真实的好吧，所以我们想要 22 00:00:49,409 --> 00:00:51,698 dominant strategy implementation we want 我们想要的主导战略实施 23 00:00:51,899 --> 00:00:53,439 to design the mechanism so that they 设计机制，使他们 24 00:00:53,640 --> 00:00:55,239 want to tell us truthfully exactly what 想真实地告诉我们什么 25 00:00:55,439 --> 00:00:56,739 their preference rankings are over the 他们的偏好排名超过 26 00:00:56,939 --> 00:00:58,570 alternatives and they don't gain at all 替代方案，他们根本没有收获 27 00:00:58,770 --> 00:01:00,908 by trying to mix up the alternatives and 通过尝试混合各种选择和 28 00:01:01,109 --> 00:01:03,189 manipulate the system okay so that's the 操纵系统好吧，那就是 29 00:01:03,390 --> 00:01:07,689 idea and in particular let's think of 的想法，尤其是让我们想到 30 00:01:07,890 --> 00:01:09,039 we've got our society with an 我们的社会 31 00:01:09,239 --> 00:01:13,599 individual's finite set of outcomes oh 个人的有限结果集哦 32 00:01:13,799 --> 00:01:16,808 and if we begin to think about designing 如果我们开始考虑设计 33 00:01:17,009 --> 00:01:19,539 mechanisms in this world and we want one 在这个世界上的机制，我们想要一个 34 00:01:19,739 --> 00:01:21,009 where every agent has a dominant 每个代理人都有支配地位 35 00:01:21,209 --> 00:01:22,390 strategy for each preference we can 我们可以针对每个偏好的策略 36 00:01:22,590 --> 00:01:25,418 invoke the revelation principle and the 引用启示原理和 37 00:01:25,618 --> 00:01:27,250 revelation principle tells us that if we 启示原理告诉我们，如果我们 38 00:01:27,450 --> 00:01:29,649 do have an indirect mechanism that has 确实有一个间接机制 39 00:01:29,849 --> 00:01:33,039 dominant strategies we can just collapse 我们可以崩溃的主导策略 40 00:01:33,239 --> 00:01:36,640 that into a social choice function a 转化为社会选择功能 41 00:01:36,840 --> 00:01:38,709 direct mechanism where people just tell 人们直接说出的直接机制 42 00:01:38,909 --> 00:01:40,719 us directly their preferences and then 我们直接按照他们的喜好 43 00:01:40,920 --> 00:01:42,009 we give them the outcomes they would 我们给他们他们想要的结果 44 00:01:42,209 --> 00:01:43,090 have gotten through the original 已经通过原始 45 00:01:43,290 --> 00:01:45,128 mechanism for each announcement of their 每次宣布的机制 46 00:01:45,328 --> 00:01:47,528 preferences so if they'd followed the 偏好设置，因此如果他们遵循 47 00:01:47,728 --> 00:01:49,659 strategies that they had had dominant 他们曾经占主导地位的策略 48 00:01:49,859 --> 00:01:51,549 strategies in the original one so this 在原来的策略，这样 49 00:01:51,750 --> 00:01:53,980 makes truth a dominant strategy so the 将真理作为主导策略，因此 50 00:01:54,180 --> 00:01:55,778 revelation principle will means that we 启示原理将意味着我们 51 00:01:55,978 --> 00:01:58,768 can without loss of generality for this 可以在不失一般性的情况下 52 00:01:58,968 --> 00:02:02,429 exercise look at social choice functions 练习看社会选择功能 53 00:02:02,629 --> 00:02:05,500 directly okay and so now what we want to 直接好了，所以现在我们要 54 00:02:05,700 --> 00:02:06,849 do is think about which social choice 要做的是考虑哪个社会选择 55 00:02:07,049 --> 00:02:09,009 functions can a society have which are 一个社会可以拥有的功能是 56 00:02:09,209 --> 00:02:11,590 going to be dominant strategy truthful 将成为主导战略的真实 57 00:02:11,789 --> 00:02:13,520 in this sense okay 从这个意义上讲可以 58 00:02:13,719 --> 00:02:19,460 well so it's these things are also known 好吧，这些东西也是众所周知的 59 00:02:19,659 --> 00:02:22,189 as non manipulable strategy proof 作为不可操纵的策略证明 60 00:02:22,389 --> 00:02:23,540 sometimes they're called straightforward 有时他们被称为简单 61 00:02:23,740 --> 00:02:25,880 mechanisms or social choice functions 机制或社会选择功能 62 00:02:26,080 --> 00:02:29,090 and the important result in this area 在这方面的重要成果 63 00:02:29,289 --> 00:02:30,740 due to Allen gibart and Mark 由于艾伦·吉伯特和马克 64 00:02:30,939 --> 00:02:33,260 Satterthwaite in the early 1970s is 1970年代初期的Satterthwaite是 65 00:02:33,460 --> 00:02:34,610 gonna say we're gonna have a really hard 会说我们将很难 66 00:02:34,810 --> 00:02:36,740 time doing this in a setting where 时间在一个设置中 67 00:02:36,939 --> 00:02:38,870 people can have any possible ranking 人们可以有任何可能的排名 68 00:02:39,069 --> 00:02:40,820 over the alternatives so let's have a 在替代方案上，让我们来 69 00:02:41,020 --> 00:02:42,650 look at that this is what's known as the 看，这就是所谓的 70 00:02:42,849 --> 00:02:45,230 givers Satterthwaite theorem and it's 给定者Satterthwaite定理，它是 71 00:02:45,430 --> 00:02:47,330 another form of an impossibility theorem 不可能定理的另一种形式 72 00:02:47,530 --> 00:02:49,400 similar to what we saw in terms of 与我们在以下方面看到的相似 73 00:02:49,599 --> 00:02:51,770 arrows theorem and Miller Satterthwaite 箭头定理和Miller Satterthwaite 74 00:02:51,969 --> 00:02:53,689 theorem so situations where we have a 定理，所以我们有一个 75 00:02:53,889 --> 00:02:55,880 set of conditions we'd like to have and 我们希望拥有的一组条件 76 00:02:56,080 --> 00:02:58,130 the theorem says it's impossible to have 定理说不可能有 77 00:02:58,330 --> 00:03:00,560 this desirable set of conditions all at 这套理想的条件 78 00:03:00,759 --> 00:03:02,810 once so what's the setting here we've 一次，那么这里的设置是什么 79 00:03:03,009 --> 00:03:05,330 got a social choice function we'd like 得到了我们想要的社交选择功能 80 00:03:05,530 --> 00:03:08,090 to have one that's mapping all possible 有一个映射所有可能的 81 00:03:08,289 --> 00:03:10,700 preferences so people have linear orders 偏好使人们拥有线性订单 82 00:03:10,900 --> 00:03:12,590 they can have any strict ranking over 他们可以有严格的排名 83 00:03:12,789 --> 00:03:16,280 candidates and we are going to look at 候选人，我们将要研究 84 00:03:16,479 --> 00:03:18,560 situations with at least three outcomes 至少有三个结果的情况 85 00:03:18,759 --> 00:03:21,080 so we have at least three candidates to 所以我们至少有三个候选人 86 00:03:21,280 --> 00:03:25,069 choose from and we're going to also look 从中选择，我们还将寻找 87 00:03:25,269 --> 00:03:27,410 at a social choice function which is on 在一个社会选择功能上 88 00:03:27,610 --> 00:03:29,030 two that means for every possible 两个意味着一切可能 89 00:03:29,229 --> 00:03:32,390 outcome there is a profile of 结果有一个配置文件 90 00:03:32,590 --> 00:03:34,310 preferences which gives you that outcome 偏好给您带来的结果 91 00:03:34,509 --> 00:03:38,300 and that condition can be satisfied 而且那个条件可以满足 92 00:03:38,500 --> 00:03:40,400 quite easily for instance if you just 例如，如果您只是 93 00:03:40,599 --> 00:03:42,950 required that your social choice 要求您的社会选择 94 00:03:43,150 --> 00:03:45,020 function be unanimous so if all 功能是一致的，所以如果全部 95 00:03:45,219 --> 00:03:48,319 individuals prefer the same alternative 个人喜欢相同的选择 96 00:03:48,519 --> 00:03:50,660 we all say we love candidate a then 我们都说我们爱候选人 97 00:03:50,860 --> 00:03:53,270 society should pick candidate a if you 如果你愿意，社会应该选择候选人 98 00:03:53,469 --> 00:03:54,920 put that minimal condition in then 然后把那个最小条件 99 00:03:55,120 --> 00:03:58,700 indeed the in this domain of preferences 确实在这个偏好领域 100 00:03:58,900 --> 00:04:01,039 C is going to be on two so if we put C将在两个点上，所以如果我们把 101 00:04:01,239 --> 00:04:02,509 those conditions in and what does the 这些条件以及什么 102 00:04:02,709 --> 00:04:04,640 theorem say the theorem says that we're 定理说定理说我们 103 00:04:04,840 --> 00:04:05,870 going to have the strategy proof in this 在这方面有策略证明 104 00:04:06,069 --> 00:04:07,789 condition truthful reporting of 有条件如实报告 105 00:04:07,989 --> 00:04:09,740 preferences as a dominant strategy for 偏好作为主导策略 106 00:04:09,939 --> 00:04:11,599 every agent at every preference profile 每个偏好配置文件中的每个业务代表 107 00:04:11,799 --> 00:04:16,699 if and only if C is dictatorial okay so 当且仅当C是独裁的就可以 108 00:04:16,899 --> 00:04:18,468 again that means here there exists some 再次这意味着这里存在一些 109 00:04:18,668 --> 00:04:21,468 particular individual I for whom the 我为之特别的个人 110 00:04:21,668 --> 00:04:24,079 choice function is just always their 选择功能永远是他们的 111 00:04:24,279 --> 00:04:26,530 favorite alternative 最喜欢的替代品 112 00:04:26,730 --> 00:04:28,120 the thing that maximizes their 最大化他们的东西 113 00:04:28,319 --> 00:04:30,879 preferences in regardless of what 偏好，无论 114 00:04:31,079 --> 00:04:32,590 anybody else says so we just pick one 有人说，所以我们只选一个 115 00:04:32,790 --> 00:04:34,660 individual we just listen to that person 个人，我们只是听那个人 116 00:04:34,860 --> 00:04:38,290 okay now in terms of the proof of this 现在就证明这一点 117 00:04:38,490 --> 00:04:41,050 it's clear that if we assign somebody to 很明显，如果我们分配某人 118 00:04:41,250 --> 00:04:42,670 be a dictator and don't listen to 成为独裁者，不听 119 00:04:42,870 --> 00:04:44,170 anybody else that's gonna be strategy 其他会成为策略的人 120 00:04:44,370 --> 00:04:45,819 proof right nobody else can make any 证明权没有其他人能做的 121 00:04:46,019 --> 00:04:47,170 difference doesn't matter what they say 他们说什么无关紧要 122 00:04:47,370 --> 00:04:49,810 and the person who is a dictator always 而独裁者总是 123 00:04:50,009 --> 00:04:51,370 wants to be truthful because they're 想要诚实，因为他们 124 00:04:51,569 --> 00:04:53,740 getting your favorite alternative the 得到你最喜欢的替代品 125 00:04:53,939 --> 00:04:55,600 converse of this theorem is is much more 这个定理的反面是更多 126 00:04:55,800 --> 00:04:57,939 difficult that part saying that if it's 很难说那是 127 00:04:58,139 --> 00:04:59,379 strategy proof then it has to be 战略证明，那么它必须是 128 00:04:59,579 --> 00:05:03,730 dictatorial and the this can be proven 独裁的，这可以证明 129 00:05:03,930 --> 00:05:07,329 by various means there are proofs that 通过各种方式可以证明 130 00:05:07,529 --> 00:05:09,790 relate this back to arrows theorem and 将此与箭头定理联系起来， 131 00:05:09,990 --> 00:05:16,139 and show that that there are similar 并证明有相似之处 132 00:05:16,339 --> 00:05:18,069 conclusions that can get in terms of the 可以得出的结论 133 00:05:18,269 --> 00:05:20,290 basic steps dilemmas that were proven 已证明的基本步骤困境 134 00:05:20,490 --> 00:05:25,230 there there's a very elegant proof by 有一个非常优雅的证明 135 00:05:25,430 --> 00:05:29,259 Salvador Barbra which works off of 萨尔瓦多·巴拉布拉（Salvador Barbra） 136 00:05:29,459 --> 00:05:31,629 individuals being pivotal in terms of 个人在以下方面至关重要 137 00:05:31,829 --> 00:05:33,129 changing their preferences and changing 改变他们的喜好并改变 138 00:05:33,329 --> 00:05:35,470 the outcome and showing that you can't 结果并显示您无法 139 00:05:35,670 --> 00:05:37,300 have too many individuals being pivotal 有太多人是关键 140 00:05:37,500 --> 00:05:39,730 at once if you are going to satisfy 如果您要立即满足 141 00:05:39,930 --> 00:05:42,129 dominant strategies so there's a basic 主导策略，所以有一个基本的 142 00:05:42,329 --> 00:05:44,259 conflict of allowing people to make 让人产生冲突 143 00:05:44,459 --> 00:05:46,240 decisions and having multiple people 决策和多人 144 00:05:46,439 --> 00:05:48,370 make decisions at the same time and 同时做出决定， 145 00:05:48,569 --> 00:05:50,590 making sure that everybody cannot 确保每个人都不能 146 00:05:50,790 --> 00:05:52,540 manipulate things by by announcing 通过宣布来操纵事情 147 00:05:52,740 --> 00:05:54,810 things falsely so we're not going to 错误的事情，所以我们不会 148 00:05:55,009 --> 00:05:57,610 explicitly offer that proof but you can 明确提供该证明，但您可以 149 00:05:57,810 --> 00:05:59,889 find various versions of this in the 在中找到各种版本 150 00:06:00,089 --> 00:06:02,650 literature and we'll leave you to look 文学，我们留给你看看 151 00:06:02,850 --> 00:06:06,610 at that directly what this means is that 直接这意味着 152 00:06:06,810 --> 00:06:08,949 any social choice function that we write 我们编写的任何社会选择功能 153 00:06:09,149 --> 00:06:11,259 down that we're interested in assuming 下来，我们有兴趣假设 154 00:06:11,459 --> 00:06:14,020 that we don't want dictatorial functions 我们不希望独裁功能 155 00:06:14,220 --> 00:06:16,000 are going to be manipulable in some 在某些方面将是可操纵的 156 00:06:16,199 --> 00:06:17,860 situations so if we're in a voting 情况，所以如果我们参加投票 157 00:06:18,060 --> 00:06:20,620 setting and we have a set of candidates 设置，我们有一组候选人 158 00:06:20,819 --> 00:06:22,480 that we're looking at and we have to 我们正在寻找，我们必须 159 00:06:22,680 --> 00:06:23,949 pick among those candidates and any 从这些候选人中挑选 160 00:06:24,149 --> 00:06:26,439 possible ordering of those is possible 这些可能的顺序是可能的 161 00:06:26,639 --> 00:06:29,860 and people's preferences regardless of 和人们的喜好，无论 162 00:06:30,060 --> 00:06:31,689 what rule we use we're going to end up 我们将使用什么规则来结束 163 00:06:31,889 --> 00:06:33,970 having people manipulate that rule in 让人们操纵这个规则 164 00:06:34,170 --> 00:06:36,520 certain situations so that's a very 在某些情况下，这是非常 165 00:06:36,720 --> 00:06:38,590 negative result in some sense it's a 从某种意义上讲，负面结果是 166 00:06:38,790 --> 00:06:40,240 damaging results and it's 破坏性的结果是 167 00:06:40,439 --> 00:06:41,560 different from arrows theorem because 与箭头定理不同，因为 168 00:06:41,759 --> 00:06:43,870 what this is doing is really looking at 这实际上是在看 169 00:06:44,069 --> 00:06:45,790 the incentives that people have and 人们拥有的激励和 170 00:06:45,990 --> 00:06:46,960 saying it's going to be difficult to 说这将很难 171 00:06:47,160 --> 00:06:49,120 beget people to be truthful when we were 当我们在一起的时候，让人变得诚实 172 00:06:49,319 --> 00:06:50,650 looking at arrows theorem there was 看着箭头定理 173 00:06:50,850 --> 00:06:52,389 nothing said about whether people were 没有人在说什么 174 00:06:52,589 --> 00:06:54,430 being truthful or not the kinds of 真实与否 175 00:06:54,629 --> 00:06:56,050 conclusions that were being reached on 得出的结论 176 00:06:56,250 --> 00:06:57,610 arrows theorem we're just saying that 箭头定理，我们只是说 177 00:06:57,810 --> 00:07:00,759 some basic independence conditions and 一些基本的独立条件和 178 00:07:00,959 --> 00:07:02,530 Pareto conditions couldn't be satisfied 无法满足帕累托条件 179 00:07:02,730 --> 00:07:04,660 by a social welfare ordering at the same 通过同时订购的社会福利 180 00:07:04,860 --> 00:07:06,670 time but presuming that you could see 时间，但假设您可以看到 181 00:07:06,870 --> 00:07:08,199 what people's preferences were as the 人们的喜好是什么 182 00:07:08,399 --> 00:07:09,939 input and this is saying that if you're 输入，这是说，如果你是 183 00:07:10,139 --> 00:07:12,100 going to make a choice it's going to be 做出选择，它将是 184 00:07:12,300 --> 00:07:13,780 difficult to get people to reveal their 很难让人透露他们的 185 00:07:13,980 --> 00:07:15,790 preferences to you in a truthful manner 真实地偏爱您 186 00:07:15,990 --> 00:07:17,949 one more thing about this and this is 关于这一点的另一件事是 187 00:07:18,149 --> 00:07:20,550 something you can verify yourself 你可以验证自己的东西 188 00:07:20,750 --> 00:07:22,329 suppose that you only had two 假设你只有两个 189 00:07:22,529 --> 00:07:25,930 alternatives then it's going to be easy 替代品，这将很容易 190 00:07:26,129 --> 00:07:29,350 to find a rule think of majority rule so 找到一个规则考虑多数规则 191 00:07:29,550 --> 00:07:30,970 is that strategy proof so imagine that 是该策略的证明，所以想象一下 192 00:07:31,170 --> 00:07:33,009 we have just two candidates and you get 我们只有两个候选人，你得到 193 00:07:33,209 --> 00:07:34,389 to vote for which one you would prefer 投票给您更喜欢的人 194 00:07:34,589 --> 00:07:37,740 and you always prefer one to the other 而你总是喜欢一个 195 00:07:37,939 --> 00:07:40,360 there there will be a variety actually 实际上会有各种各样 196 00:07:40,560 --> 00:07:43,468 of strategy proof rules in that setting 在那种情况下的策略证明规则 197 00:07:43,668 --> 00:07:50,560 if C is not on - then we are ignoring 如果C没有打开-那么我们将忽略 198 00:07:50,759 --> 00:07:53,650 certain outcomes then you're going to 某些结果，那么您将 199 00:07:53,850 --> 00:07:56,110 have some more limited conclusions here 这里有一些更有限的结论 200 00:07:56,310 --> 00:07:57,218 that things are going to be stick 事情会坚持下去 201 00:07:57,418 --> 00:07:59,319 tutorial but only on the range of the 教程，但仅适用于 202 00:07:59,519 --> 00:08:02,230 outcome function if at least if it still 结果函数，如果至少仍然 203 00:08:02,430 --> 00:08:04,689 has at least three alternatives in it so 至少有三个选择 204 00:08:04,889 --> 00:08:07,060 there's some limitations on this but in 有一些限制，但在 205 00:08:07,259 --> 00:08:08,468 terms of really getting around this kind 真正解决这类问题的条件 206 00:08:08,668 --> 00:08:12,340 of negative result there's various ways 负面结果有多种方式 207 00:08:12,540 --> 00:08:15,009 we can think of doing this um one is to 我们可以想到做这个是 208 00:08:15,209 --> 00:08:17,199 use a weaker form of implementation so 使用较弱的实现方式 209 00:08:17,399 --> 00:08:19,509 here we're we were asking for dominant 在这里，我们是在要求主导 210 00:08:19,709 --> 00:08:21,129 strategies for all individuals at all 面向所有个人的策略 211 00:08:21,329 --> 00:08:23,439 preferences we could work instead for 我们可以代替的偏好 212 00:08:23,639 --> 00:08:25,090 something like Bayes Nash implementation 类似于Bayes Nash的实现 213 00:08:25,290 --> 00:08:27,160 Bayesian implementation where we ask 我们问的贝叶斯实现 214 00:08:27,360 --> 00:08:31,509 people just to have a best response - to 人们只是为了做出最好的回应- 215 00:08:31,709 --> 00:08:33,639 announce truthfully given that everyone 诚实地宣布，因为每个人 216 00:08:33,839 --> 00:08:36,909 else's and that'll open some doors for 否则，这将为 217 00:08:37,110 --> 00:08:38,349 us that's going to be much more 我们将会更多 218 00:08:38,549 --> 00:08:39,939 demanding in terms of an equilibrium 要求均衡 219 00:08:40,139 --> 00:08:41,859 concept and the beauty of dominant 概念和优势之美 220 00:08:42,059 --> 00:08:43,479 strategies is people don't have to worry 策略是人们不必担心 221 00:08:43,679 --> 00:08:45,009 about what other people are doing and 关于别人在做什么， 222 00:08:45,210 --> 00:08:47,199 they don't have to know or have beliefs 他们不必知道或有信仰 223 00:08:47,399 --> 00:08:49,500 about what's going on Bayes Nash 关于贝叶斯·纳什（Bayes Nash）发生的事情 224 00:08:49,700 --> 00:08:52,000 structure a Bayesian Nash structure is 贝叶斯Nash结构是 225 00:08:52,200 --> 00:08:54,128 much more demanding and that 要求更高， 226 00:08:54,328 --> 00:08:58,988 since we could relax the assumption that 因为我们可以放宽假设 227 00:08:59,188 --> 00:09:01,209 people have arbitrary preferences and 人们有任意的偏好， 228 00:09:01,409 --> 00:09:02,649 look at more structured settings and 看看更结构化的设置 229 00:09:02,850 --> 00:09:04,988 indeed when we do that we're going to 确实，当我们这样做时，我们将 230 00:09:05,188 --> 00:09:07,719 find much more interesting and positive 发现更多有趣和正面的 231 00:09:07,919 --> 00:09:11,709 results in terms of rules that we can 根据我们可以制定的规则 232 00:09:11,909 --> 00:09:13,448 apply so more interesting rules I should 应用更有趣的规则 233 00:09:13,649 --> 00:09:15,188 say not more interesting results that 说不出更有趣的结果 234 00:09:15,389 --> 00:09:16,478 give or Satterthwaite theorem is a very Give或Satterthwaite定理是一个非常 235 00:09:16,678 --> 00:09:18,368 interesting result but we'll find more 有趣的结果，但我们会发现更多 236 00:09:18,568 --> 00:09:20,308 interesting rules that we can work with 我们可以使用的有趣规则 237 00:09:20,509 --> 00:09:23,198 we've already seen one in fact median 我们已经看过一个事实上的中位数 238 00:09:23,399 --> 00:09:26,769 voting on a single peak domain so as we 在单个高峰域上投票 239 00:09:26,970 --> 00:09:29,048 mentioned there if you're asked for your 提到那里，如果您被要求 240 00:09:29,249 --> 00:09:31,719 preferences you have no reason to try 您没有理由尝试的偏好 241 00:09:31,919 --> 00:09:33,578 and distort your preferences the median 并扭曲您的偏好中位数 242 00:09:33,778 --> 00:09:34,988 peak wins and the only way to change 高峰制胜和改变的唯一途径 243 00:09:35,188 --> 00:09:39,248 that is to flip over and announce 就是翻过来宣布 244 00:09:39,448 --> 00:09:40,478 something on the other side which would 另一边的东西 245 00:09:40,678 --> 00:09:42,608 be worse for a given individual you 对于一个给定的人你会更糟 246 00:09:42,808 --> 00:09:44,258 could also take the max of the peaks you 也可能会占用您最大的山峰 247 00:09:44,458 --> 00:09:45,639 could do instead of median voting have 可以代替中位数投票 248 00:09:45,839 --> 00:09:48,519 maximum voting so whoever has the 最高投票权，无论谁拥有 249 00:09:48,720 --> 00:09:51,519 maximum peak or the minimum peak or any 最大峰或最小峰或任何 250 00:09:51,720 --> 00:09:53,738 order statistics so single peak domains 订单统计，因此单峰域 251 00:09:53,938 --> 00:09:55,209 are going to be settings where what 将要设置在什么地方 252 00:09:55,409 --> 00:09:56,738 we've done is we've limited the set of 我们要做的是限制了 253 00:09:56,938 --> 00:09:58,538 preferences so not any ordering over 偏好，因此没有任何排序 254 00:09:58,739 --> 00:10:00,578 candidates is allowed any longer and 候选人被允许再 255 00:10:00,778 --> 00:10:03,218 once you do that then it's easier to 一旦这样做，就更容易 256 00:10:03,418 --> 00:10:06,788 design strategy proof rules another 设计策略证明另有规定 257 00:10:06,989 --> 00:10:09,279 setting I'm trade so imagine that you 设置我要交易，所以想象你 258 00:10:09,480 --> 00:10:12,038 have an indivisible good you have to a 有一个不可分割的好处，你必须 259 00:10:12,239 --> 00:10:14,168 buyer and a seller and they might have 买方和卖方，他们可能有 260 00:10:14,369 --> 00:10:16,748 private values for how much they value 私人价值观 261 00:10:16,948 --> 00:10:19,178 the good and you're trying to get trade 的好处，你正在努力获得贸易 262 00:10:19,379 --> 00:10:22,748 to go on one mechanism that works in 进行一种有效的机制 263 00:10:22,948 --> 00:10:25,149 that situation is just to fix a price so 这种情况只是为了定价 264 00:10:25,350 --> 00:10:29,468 say you can trade the price at at a 说您可以以 265 00:10:29,668 --> 00:10:31,928 price of 10 so individuals say at a 10个人的价格， 266 00:10:32,129 --> 00:10:33,668 price of 10 am I willing to trade or not 我愿意交易或不交易的价格为上午10点 267 00:10:33,869 --> 00:10:35,798 and now there's a simple decision you 现在有一个简单的决定 268 00:10:35,999 --> 00:10:37,779 can't influence the price all you can do 不能影响价格 269 00:10:37,980 --> 00:10:39,368 is influence whether you actually trade 是否真的进行交易会产生影响 270 00:10:39,568 --> 00:10:41,649 or not and so then it's you have an 还是没有，所以那是你有一个 271 00:10:41,850 --> 00:10:43,328 incentive to say truthfully do you 激励你说实话 272 00:10:43,528 --> 00:10:44,948 really want the trade or do you not and 真的想要交易还是不想要 273 00:10:45,149 --> 00:10:47,139 then trade if both of the agents want 然后如果两个代理商都想要交易 274 00:10:47,339 --> 00:10:48,909 the trade so there you can design a 贸易，所以你可以设计一个 275 00:10:49,110 --> 00:10:50,978 dominant strategy mechanism there's 主导策略机制有 276 00:10:51,178 --> 00:10:52,269 gonna be some inefficiencies associated 可能会导致效率低下 277 00:10:52,470 --> 00:10:54,008 with that you're not going to have trade 这样你就不会有交易 278 00:10:54,208 --> 00:10:55,779 occurring in all the circumstances that 在所有情况下 279 00:10:55,980 --> 00:10:58,149 you'd like but at least you've got 你想要但至少你有 280 00:10:58,350 --> 00:11:00,399 dominant strategies and what we'll take 主导策略以及我们将采取的措施 281 00:11:00,600 --> 00:11:02,978 a closer look at these things we're 仔细看看这些东西 282 00:11:03,178 --> 00:11:04,959 gonna see a whole series of other types 会看到一系列其他类型的 283 00:11:05,159 --> 00:11:06,668 of rules that we'll look at the Vickery 规则，我们将看维克 284 00:11:06,869 --> 00:11:08,318 Clark grow of schemes and other kinds of 克拉克计划和其他种类的成长 285 00:11:08,519 --> 00:11:10,328 schemes and when we look and narrow in 方案，当我们寻找并缩小范围时 286 00:11:10,528 --> 00:11:11,798 the kinds of settings we're looking at 我们正在查看的设置种类 287 00:11:11,999 --> 00:11:13,838 with more structure on preferences we'll 通过偏好的更多结构，我们将 288 00:11:14,038 --> 00:11:15,698 have a whole series of interesting 有一系列有趣的事情 289 00:11:15,899 --> 00:11:18,218 dominant strategy compatible mechanisms 优势战略兼容机制 290 00:11:18,418 --> 00:11:20,168 which are going to be present and we'll 这将要存在，我们将 291 00:11:20,369 --> 00:11:22,568 take a look at particular kinds of 看一下特定种类的 292 00:11:22,769 --> 00:11:23,618 environments where that's going to be 这将是的环境 293 00:11:23,818 --> 00:11:28,818 possible we'll be next up 可能我们会下一个