hi folks its Matt again and we're going 嗨，大家好，Matt，我们要去
to talk now about dominant strategy 现在谈论主导策略
implementation so the idea that we're 实施，所以我们
looking at is we have a society we have 看着我们有一个社会
to make a decision and we're trying to 做出决定，我们正在努力
design a mechanism that is going to take 设计需要采取的机制
people's preferences and give us 人们的喜好并给我们
outcomes and in particular let's start 结果，特别是让我们开始
by looking at a situation where we've 通过观察我们已经
got a full set of alternatives and any 有全套的替代品和任何
possible ranking over those things so 可能对这些东西进行排名
for instance we have a set of candidates 例如我们有一组候选人
that we need to pick from say four or 我们需要从说四或
five six candidates okay so we think 五六个候选人好吧，我们认为
about the voting rules that we looked at 关于我们看过的投票规则
earlier now we've got to make a choice 现在早些时候，我们必须做出选择
over these candidates and in particular 这些候选人，尤其是
what we'd like is when we ask people 我们想要的是当我们问别人时
that they have no difficulties in 他们没有困难
deciding what they should announce they 决定他们应该宣布什么
should just be truthful okay so we want 应该是真实的好吧，所以我们想要
dominant strategy implementation we want 我们想要的主导战略实施
to design the mechanism so that they 设计机制，使他们
want to tell us truthfully exactly what 想真实地告诉我们什么
their preference rankings are over the 他们的偏好排名超过
alternatives and they don't gain at all 替代方案，他们根本没有收获
by trying to mix up the alternatives and 通过尝试混合各种选择和
manipulate the system okay so that's the 操纵系统好吧，那就是
idea and in particular let's think of 的想法，尤其是让我们想到
we've got our society with an 我们的社会
individual's finite set of outcomes oh 个人的有限结果集哦
and if we begin to think about designing 如果我们开始考虑设计
mechanisms in this world and we want one 在这个世界上的机制，我们想要一个
where every agent has a dominant 每个代理人都有支配地位
strategy for each preference we can 我们可以针对每个偏好的策略
invoke the revelation principle and the 引用启示原理和
revelation principle tells us that if we 启示原理告诉我们，如果我们
do have an indirect mechanism that has 确实有一个间接机制
dominant strategies we can just collapse 我们可以崩溃的主导策略
that into a social choice function a 转化为社会选择功能
direct mechanism where people just tell 人们直接说出的直接机制
us directly their preferences and then 我们直接按照他们的喜好
we give them the outcomes they would 我们给他们他们想要的结果
have gotten through the original 已经通过原始
mechanism for each announcement of their 每次宣布的机制
preferences so if they'd followed the 偏好设置，因此如果他们遵循
strategies that they had had dominant 他们曾经占主导地位的策略
strategies in the original one so this 在原来的策略，这样
makes truth a dominant strategy so the 将真理作为主导策略，因此
revelation principle will means that we 启示原理将意味着我们
can without loss of generality for this 可以在不失一般性的情况下
exercise look at social choice functions 练习看社会选择功能
directly okay and so now what we want to 直接好了，所以现在我们要
do is think about which social choice 要做的是考虑哪个社会选择
functions can a society have which are 一个社会可以拥有的功能是
going to be dominant strategy truthful 将成为主导战略的真实
in this sense okay 从这个意义上讲可以
well so it's these things are also known 好吧，这些东西也是众所周知的
as non manipulable strategy proof 作为不可操纵的策略证明
sometimes they're called straightforward 有时他们被称为简单
mechanisms or social choice functions 机制或社会选择功能
and the important result in this area 在这方面的重要成果
due to Allen gibart and Mark 由于艾伦·吉伯特和马克
Satterthwaite in the early 1970s is 1970年代初期的Satterthwaite是
gonna say we're gonna have a really hard 会说我们将很难
time doing this in a setting where 时间在一个设置中
people can have any possible ranking 人们可以有任何可能的排名
over the alternatives so let's have a 在替代方案上，让我们来
look at that this is what's known as the 看，这就是所谓的
givers Satterthwaite theorem and it's 给定者Satterthwaite定理，它是
another form of an impossibility theorem 不可能定理的另一种形式
similar to what we saw in terms of 与我们在以下方面看到的相似
arrows theorem and Miller Satterthwaite 箭头定理和Miller Satterthwaite
theorem so situations where we have a 定理，所以我们有一个
set of conditions we'd like to have and 我们希望拥有的一组条件
the theorem says it's impossible to have 定理说不可能有
this desirable set of conditions all at 这套理想的条件
once so what's the setting here we've 一次，那么这里的设置是什么
got a social choice function we'd like 得到了我们想要的社交选择功能
to have one that's mapping all possible 有一个映射所有可能的
preferences so people have linear orders 偏好使人们拥有线性订单
they can have any strict ranking over 他们可以有严格的排名
candidates and we are going to look at 候选人，我们将要研究
situations with at least three outcomes 至少有三个结果的情况
so we have at least three candidates to 所以我们至少有三个候选人
choose from and we're going to also look 从中选择，我们还将寻找
at a social choice function which is on 在一个社会选择功能上
two that means for every possible 两个意味着一切可能
outcome there is a profile of 结果有一个配置文件
preferences which gives you that outcome 偏好给您带来的结果
and that condition can be satisfied 而且那个条件可以满足
quite easily for instance if you just 例如，如果您只是
required that your social choice 要求您的社会选择
function be unanimous so if all 功能是一致的，所以如果全部
individuals prefer the same alternative 个人喜欢相同的选择
we all say we love candidate a then 我们都说我们爱候选人
society should pick candidate a if you 如果你愿意，社会应该选择候选人
put that minimal condition in then 然后把那个最小条件
indeed the in this domain of preferences 确实在这个偏好领域
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
those conditions in and what does the 这些条件以及什么
theorem say the theorem says that we're 定理说定理说我们
going to have the strategy proof in this 在这方面有策略证明
condition truthful reporting of 有条件如实报告
preferences as a dominant strategy for 偏好作为主导策略
every agent at every preference profile 每个偏好配置文件中的每个业务代表
if and only if C is dictatorial okay so 当且仅当C是独裁的就可以
again that means here there exists some 再次这意味着这里存在一些
particular individual I for whom the 我为之特别的个人
choice function is just always their 选择功能永远是他们的
favorite alternative 最喜欢的替代品
the thing that maximizes their 最大化他们的东西
preferences in regardless of what 偏好，无论
anybody else says so we just pick one 有人说，所以我们只选一个
individual we just listen to that person 个人，我们只是听那个人
okay now in terms of the proof of this 现在就证明这一点
it's clear that if we assign somebody to 很明显，如果我们分配某人
be a dictator and don't listen to 成为独裁者，不听
anybody else that's gonna be strategy 其他会成为策略的人
proof right nobody else can make any 证明权没有其他人能做的
difference doesn't matter what they say 他们说什么无关紧要
and the person who is a dictator always 而独裁者总是
wants to be truthful because they're 想要诚实，因为他们
getting your favorite alternative the 得到你最喜欢的替代品
converse of this theorem is is much more 这个定理的反面是更多
difficult that part saying that if it's 很难说那是
strategy proof then it has to be 战略证明，那么它必须是
dictatorial and the this can be proven 独裁的，这可以证明
by various means there are proofs that 通过各种方式可以证明
relate this back to arrows theorem and 将此与箭头定理联系起来，
and show that that there are similar 并证明有相似之处
conclusions that can get in terms of the 可以得出的结论
basic steps dilemmas that were proven 已证明的基本步骤困境
there there's a very elegant proof by 有一个非常优雅的证明
Salvador Barbra which works off of 萨尔瓦多·巴拉布拉（Salvador Barbra）
individuals being pivotal in terms of 个人在以下方面至关重要
changing their preferences and changing 改变他们的喜好并改变
the outcome and showing that you can't 结果并显示您无法
have too many individuals being pivotal 有太多人是关键
at once if you are going to satisfy 如果您要立即满足
dominant strategies so there's a basic 主导策略，所以有一个基本的
conflict of allowing people to make 让人产生冲突
decisions and having multiple people 决策和多人
make decisions at the same time and 同时做出决定，
making sure that everybody cannot 确保每个人都不能
manipulate things by by announcing 通过宣布来操纵事情
things falsely so we're not going to 错误的事情，所以我们不会
explicitly offer that proof but you can 明确提供该证明，但您可以
find various versions of this in the 在中找到各种版本
literature and we'll leave you to look 文学，我们留给你看看
at that directly what this means is that 直接这意味着
any social choice function that we write 我们编写的任何社会选择功能
down that we're interested in assuming 下来，我们有兴趣假设
that we don't want dictatorial functions 我们不希望独裁功能
are going to be manipulable in some 在某些方面将是可操纵的
situations so if we're in a voting 情况，所以如果我们参加投票
setting and we have a set of candidates 设置，我们有一组候选人
that we're looking at and we have to 我们正在寻找，我们必须
pick among those candidates and any 从这些候选人中挑选
possible ordering of those is possible 这些可能的顺序是可能的
and people's preferences regardless of 和人们的喜好，无论
what rule we use we're going to end up 我们将使用什么规则来结束
having people manipulate that rule in 让人们操纵这个规则
certain situations so that's a very 在某些情况下，这是非常
negative result in some sense it's a 从某种意义上讲，负面结果是
damaging results and it's 破坏性的结果是
different from arrows theorem because 与箭头定理不同，因为
what this is doing is really looking at 这实际上是在看
the incentives that people have and 人们拥有的激励和
saying it's going to be difficult to 说这将很难
beget people to be truthful when we were 当我们在一起的时候，让人变得诚实
looking at arrows theorem there was 看着箭头定理
nothing said about whether people were 没有人在说什么
being truthful or not the kinds of 真实与否
conclusions that were being reached on 得出的结论
arrows theorem we're just saying that 箭头定理，我们只是说
some basic independence conditions and 一些基本的独立条件和
Pareto conditions couldn't be satisfied 无法满足帕累托条件
by a social welfare ordering at the same 通过同时订购的社会福利
time but presuming that you could see 时间，但假设您可以看到
what people's preferences were as the 人们的喜好是什么
input and this is saying that if you're 输入，这是说，如果你是
going to make a choice it's going to be 做出选择，它将是
difficult to get people to reveal their 很难让人透露他们的
preferences to you in a truthful manner 真实地偏爱您
one more thing about this and this is 关于这一点的另一件事是
something you can verify yourself 你可以验证自己的东西
suppose that you only had two 假设你只有两个
alternatives then it's going to be easy 替代品，这将很容易
to find a rule think of majority rule so 找到一个规则考虑多数规则
is that strategy proof so imagine that 是该策略的证明，所以想象一下
we have just two candidates and you get 我们只有两个候选人，你得到
to vote for which one you would prefer 投票给您更喜欢的人
and you always prefer one to the other 而你总是喜欢一个
there there will be a variety actually 实际上会有各种各样
of strategy proof rules in that setting 在那种情况下的策略证明规则
if C is not on - then we are ignoring 如果C没有打开-那么我们将忽略
certain outcomes then you're going to 某些结果，那么您将
have some more limited conclusions here 这里有一些更有限的结论
that things are going to be stick 事情会坚持下去
tutorial but only on the range of the 教程，但仅适用于
outcome function if at least if it still 结果函数，如果至少仍然
has at least three alternatives in it so 至少有三个选择
there's some limitations on this but in 有一些限制，但在
terms of really getting around this kind 真正解决这类问题的条件
of negative result there's various ways 负面结果有多种方式
we can think of doing this um one is to 我们可以想到做这个是
use a weaker form of implementation so 使用较弱的实现方式
here we're we were asking for dominant 在这里，我们是在要求主导
strategies for all individuals at all 面向所有个人的策略
preferences we could work instead for 我们可以代替的偏好
something like Bayes Nash implementation 类似于Bayes Nash的实现
Bayesian implementation where we ask 我们问的贝叶斯实现
people just to have a best response - to 人们只是为了做出最好的回应-
announce truthfully given that everyone 诚实地宣布，因为每个人
else's and that'll open some doors for 否则，这将为
us that's going to be much more 我们将会更多
demanding in terms of an equilibrium 要求均衡
concept and the beauty of dominant 概念和优势之美
strategies is people don't have to worry 策略是人们不必担心
about what other people are doing and 关于别人在做什么，
they don't have to know or have beliefs 他们不必知道或有信仰
about what's going on Bayes Nash 关于贝叶斯·纳什（Bayes Nash）发生的事情
structure a Bayesian Nash structure is 贝叶斯Nash结构是
much more demanding and that 要求更高，
since we could relax the assumption that 因为我们可以放宽假设
people have arbitrary preferences and 人们有任意的偏好，
look at more structured settings and 看看更结构化的设置
indeed when we do that we're going to 确实，当我们这样做时，我们将
find much more interesting and positive 发现更多有趣和正面的
results in terms of rules that we can 根据我们可以制定的规则
apply so more interesting rules I should 应用更有趣的规则
say not more interesting results that 说不出更有趣的结果
give or Satterthwaite theorem is a very Give或Satterthwaite定理是一个非常
interesting result but we'll find more 有趣的结果，但我们会发现更多
interesting rules that we can work with 我们可以使用的有趣规则
we've already seen one in fact median 我们已经看过一个事实上的中位数
voting on a single peak domain so as we 在单个高峰域上投票
mentioned there if you're asked for your 提到那里，如果您被要求
preferences you have no reason to try 您没有理由尝试的偏好
and distort your preferences the median 并扭曲您的偏好中位数
peak wins and the only way to change 高峰制胜和改变的唯一途径
that is to flip over and announce 就是翻过来宣布
something on the other side which would 另一边的东西
be worse for a given individual you 对于一个给定的人你会更糟
could also take the max of the peaks you 也可能会占用您最大的山峰
could do instead of median voting have 可以代替中位数投票
maximum voting so whoever has the 最高投票权，无论谁拥有
maximum peak or the minimum peak or any 最大峰或最小峰或任何
order statistics so single peak domains 订单统计，因此单峰域
are going to be settings where what 将要设置在什么地方
we've done is we've limited the set of 我们要做的是限制了
preferences so not any ordering over 偏好，因此没有任何排序
candidates is allowed any longer and 候选人被允许再
once you do that then it's easier to 一旦这样做，就更容易
design strategy proof rules another 设计策略证明另有规定
setting I'm trade so imagine that you 设置我要交易，所以想象你
have an indivisible good you have to a 有一个不可分割的好处，你必须
buyer and a seller and they might have 买方和卖方，他们可能有
private values for how much they value 私人价值观
the good and you're trying to get trade 的好处，你正在努力获得贸易
to go on one mechanism that works in 进行一种有效的机制
that situation is just to fix a price so 这种情况只是为了定价
say you can trade the price at at a 说您可以以
price of 10 so individuals say at a 10个人的价格，
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
and now there's a simple decision you 现在有一个简单的决定
can't influence the price all you can do 不能影响价格
is influence whether you actually trade 是否真的进行交易会产生影响
or not and so then it's you have an 还是没有，所以那是你有一个
incentive to say truthfully do you 激励你说实话
really want the trade or do you not and 真的想要交易还是不想要
then trade if both of the agents want 然后如果两个代理商都想要交易
the trade so there you can design a 贸易，所以你可以设计一个
dominant strategy mechanism there's 主导策略机制有
gonna be some inefficiencies associated 可能会导致效率低下
with that you're not going to have trade 这样你就不会有交易
occurring in all the circumstances that 在所有情况下
you'd like but at least you've got 你想要但至少你有
dominant strategies and what we'll take 主导策略以及我们将采取的措施
a closer look at these things we're 仔细看看这些东西
gonna see a whole series of other types 会看到一系列其他类型的
of rules that we'll look at the Vickery 规则，我们将看维克
Clark grow of schemes and other kinds of 克拉克计划和其他种类的成长
schemes and when we look and narrow in 方案，当我们寻找并缩小范围时
the kinds of settings we're looking at 我们正在查看的设置种类
with more structure on preferences we'll 通过偏好的更多结构，我们将
have a whole series of interesting 有一系列有趣的事情
dominant strategy compatible mechanisms 优势战略兼容机制
which are going to be present and we'll 这将要存在，我们将
take a look at particular kinds of 看一下特定种类的
environments where that's going to be 这将是的环境
possible we'll be next up 可能我们会下一个