Mechanism Design, Auctions, Voting, Bargaining and Ethics in AI

Cooperative game primitives. Let $N=\{1,\dots ,n\}$ be the set of players. The characteristic function $v:2^N\to \mathbb{R}$ assigns to each coalition $S\subseteq N$ its worth $v(S)$, with $v(\varnothing )=0$. An allocation $x=(x_1,\dots ,x_n)$ distributes the grand coalition value $v(N)$ so that ${\sum }_{i\in N}{x}_i=v(N)$ and $x_i\ge v(\{i\})$ for individual rationality.

Two solution ideas dominate:

The Shapley value ${\varphi }_i(v)$ is a fair division rule built from four axioms — efficiency, symmetry, dummy, and additivity. It gives each player the average of their marginal contributions over all possible arrival orders.

The core is the set of allocations where no subgroup can profitably defect:

$$\text{Core}(v)=\left\{x:\sum _{i\in N}{x}_i=v(N),\sum _{i\in S}{x}_i\ge v(S)\text{for every }S\subseteq N\right\}$$

When a division lies in the core, the grand coalition holds together; when it lies outside, some subgroup $S$ can leave and guarantee $v(S)$ on its own, so the split is unstable. The Shapley value is always fair by axioms, but it need not lie in the core. The core may be empty.

Fairness axioms leading to Shapley (recap): Efficiency says the whole pie is shared; Symmetry says interchangeable players receive equal shares; Dummy says a player who never adds value receives zero; Additivity says the value for the sum of two games is the sum of the values. Only the Shapley formula satisfies all four together.

The Shapley value for player $i$ is

$${\varphi }_i(v)=\sum _{S\subseteq N\setminus \{i\}}\frac{|S|!(n-|S|-1)!}{n!}[v(S\cup \{i\})-v(S)]$$

where $v(S\cup \{i\})-v(S)$ is the marginal contribution of $i$ when joining $S$. Every permutation of players is equally likely, and the term $\frac{|S|!(n-|S|-1)!}{n!}$ is the fraction of permutations where precisely the set $S$ arrives before $i$.

Intuition step by step: list all $n!$ orders, watch how much the total jumps when $i$ walks in, average those jumps. That average is the fair share.

Mechanism design is the task of engineering specific rules, in effect designing a game, for a collection of self-interested agents to participate so that the outcome the designer wants is achieved. Where game theory takes the rules as given and predicts behaviour, mechanism design reverse-engineers the rules from the desired outcome.

Think of it as working backwards: start from the outcome you want — for example, tasks allocated to the most capable agents at honest costs, or spectrum allocated to the highest true valuation — then craft the rules that lead self-interested behaviour toward that outcome. The designer chooses the strategy language, the centre, and the outcome rule, and agents then play within that game.

This shift is described as moving from individual agent design to structural configuration of the whole system. The objective shifts toward creating the right incentives rather than toward tuning a single decision maker.

A mechanism is not an informal handshake; it is a fully specified game defined by three components that together determine what agents can do and what happens as a result.

1. Strategy language (or message space). The language and allowed protocols that agents must adopt when they report or act. This is not the low-level software message format, it is the decision-making vocabulary: what an agent is allowed to say about its preferences, costs, or bids. For example, in an auction the language might be "submit a single non-negative number $B_i$" or "submit a full ranking over alternatives." The richness of this language determines whether agents can express their true preferences fully.

1. Centre (center, or mediator / auctioneer). A designated agent responsible for collecting reports, bids, and strategies and for coordinating the process. The centre (center) gathers inputs and applies the rule. The centre is assumed to be trusted and to commit to the announced rule.

1. Outcome rule (or social choice function plus payment). A universally transparent, deterministic rule used by the centre to resolve final payoffs and allocations. Everyone knows the rule in advance and the rule maps reported strategies to results — who gets the item and how much is paid, which ranking wins, or how surplus is divided. Formally, if reports are $\hat{\theta }=({\hat{\theta }}_1,\dots ,{\hat{\theta }}_n)$, the outcome rule is $f(\hat{\theta })$ plus transfers $p(\hat{\theta })$.

These three together define the game that agents play. Changing any one pillar changes the game.

• Strategy-proof mechanism. A game structure where every agent possesses a dominant strategy that yields the best possible payoff, irrespective of how other agents behave. Having a dominant strategy means the agent does not need to guess what others will do. Formally, for every agent $i$ there exists $s_i^{\ast }$ such that for all $s_i$ and all $s_{-i}$,

$$u_i(s_i^{\ast },s_{-i})\ge u_i(s_i,s_{-i})$$

• Truth-revealing (or incentive-compatible / strategy-proof in the direct sense) mechanism. A strategy-proof mechanism where an agent's dominant strategy requires them to report true preferences ${\hat{\theta }}_i={\theta }_i$. In such a mechanism, honesty is the best move irrespective of others.

• Revelation principle. The foundational theorem stating that any mechanism (even an indirect one with complex strategies) can be mathematically transformed into an equivalent, structurally stable, direct truth-revealing mechanism that yields the same outcome. In plain terms, instead of dealing with a complex game where agents might manipulate, a designer can construct a direct truth-revealing game that replicates the same equilibrium outcome. The session noted this is powerful in theory but not always easy to build in practice because the direct mechanism may be computationally hard or require unrealistic commitment.

The hierarchy: every truth-revealing mechanism is strategy-proof, but not every strategy-proof mechanism is truth-revealing. The revelation principle says we may without loss of generality focus on direct truth-revealing designs when searching for achievable outcomes.

Purpose: Allocate a task from a manager that lacks capability, time, or cost advantage to the best contractor, using decentralized bidding rather than central planning.

Inputs and outputs: Input is a task specification with quality requirements, deadlines, and eligibility constraints; outputs are a set of bids $B_j$ each containing price and terms (e.g., earliest start time), and finally an award decision and execution commitment.

Steps:

1. Problem recognition. An agent determines that the goal requires cooperative help. If one agent alone can solve the goal, cooperation is not needed. Triggers include lacking capability, lacking a resource, or recognizing that outsourcing is faster, cheaper, or more accurate. This is a local decision based on self-knowledge.

1. Announcement. The agent acts as a manager and broadcasts an announcement message containing task specification data, deadlines, quality requirements, and bidding instructions. The broadcast is one-to-many; the strategy language here is the task description plus the bid format.

1. Bidding. Recipient agents receive the announcement and compare the specification against their own capabilities and preferences. If willing and able, they submit formal bids detailing capability and terms (price, availability, confidence). If not eligible, they may remain silent. The cooperative game theory tension is most active in this phase, because how agents bid — how honestly they reveal costs — shapes the outcome. Bidding is strategic: an idle agent may bid low to win work, a busy agent may add delay cost.

1. Award. The manager evaluates received bids via the outcome rule, selects a suitable contractor (which is simply an agent chosen to do the work), returns an award notification (and rejections to others), and the chosen bidder takes formal responsibility for execution. The contractor may then itself become a manager for subtasks, so the pattern can nest recursively.

This flow repeats whenever new tasks need sharing, forming a market-like loop that needs no central planner beyond the per-task manager role.

Two categories of valuation were distinguished. The distinction determines how bidders reason and whether naive bidding causes a winner's curse.

• Private value. The item's value depends entirely on the agent's subjective preference and is independent of others' values. Example given: individual taste in artwork. If agents are asked to value an artwork, each valuation $V_i$ reflects personal likes and dislikes. The value is subjective and differs across agents for that reason alone. Formally, $V_i$ is drawn independently and knowing another bidder's valuation tells you nothing about your own. Your utility if you win at price $p$ is $V_i-p$, independent of others.

• Common value. The item has an objective but uncertain market value $V$ that is identical for all agents, but agents hold different estimates ${\hat{V}}_i$ of that single true value because they have asymmetric information. Examples: oil drilling rights or a property's market rate. The session noted that even a house has two parts: one private (your personal liking for the garden) and one common (the resale market rate every buyer eventually faces). For a pure common value, $V_i=V$ for all $i$; differences in bids come from different information, not different tastes. One person's estimate may differ from another's, even though the underlying true value is common. The winner who most overestimated $V$ can suffer the winner's curse — paying more than the true common value.

Many real auctions are interdependent or mixed: an item has both a private taste component and a common market component, so $V_i=c_i+V_{\text{common}}+{ϵ}_i$.

An auction mechanism is efficient (or allocatively efficient) if it allocates the resource to the agent who possesses the highest true underlying valuation:

$$\text{allocate to }{i}^{\ast }\text{ where }{i}^{\ast }=\arg \underset{i}{\max }{V}_i$$

In other words, the item should end up with the bidder who values it most in truth, not merely who shouted loudest or who guessed highest under common values. Efficiency is about real welfare ${\sum }_i{u}_i$, not about reported bids. If bids equal true values $B_i=V_i$, the winner is efficient; if bidders shade or lie, allocation can be inefficient even when the payment rule looks reasonable.

Connection to the three pillars: the strategy language is how bids are expressed (a single number $B_i$ in the simplest case), the centre is the auctioneer who collects $B_i$, and the outcome rule maps the vector $(B_1,\dots ,B_n)$ to a winner and a price $p$. Efficiency depends on whether the equilibrium of that game induces truthful or ranking-preserving bids.

Verbal description: the auction starts with a baseline reserve price and monotonically increases by a fixed increment as long as multiple agents signal willingness to pay. The auction concludes when only one bidder remains willing, who wins at the price where the second-last dropped out. The process is open — everyone sees the current price and who remains — and ascending — prices never go down.

Formalized: let $B_{\min }$ be the baseline reserve price and let $D$ be the fixed increment. Prices visited are

$$B_{\min },B_{\min }+D,B_{\min }+2D,\dots ,B_{\min }+kD$$

Bidders signal willingness at each level. The last remaining bidder wins at the price where the second-last dropped out. In the simplest private-value view, the final price lands one increment above the second-highest valuation.

Blocks of numbers mentioned: a house auction starting at $3,000,000$ or $5,000,000$ and rising through bids such as $500,000$, $1,000,000$, and so on. An IPL bid rises from a base price by increments of $D$ and never decreases; it only increases. The increment $D$ may be fixed by rules or chosen by the standing high bidder within allowed steps.

1. Dominant strategy in English auction. Under private values with no collusion, bidders have a straightforward dominant strategy: continue bidding as long as the current price is less than the true valuation $V_i$. Once the current price $p$ exceeds $V_i$, stop bidding and let others continue. In the IPL image, each team has a max cap it will spend for a player. As long as $p<V_i$, staying in can only help; when $p>V_i$, winning would give negative utility $V_i-p<0$.

Condition:

$$\text{stay in if }p<V_i,\text{drop out if }p>V_i$$

At $p=V_i$ the bidder is indifferent. This strategy is dominant because it does not depend on what others do — it only compares the public price to private $V_i$.

1. Outcome value. The agent with the highest valuation wins, and the price approximates the second-highest valuation plus an increment. Formally, if bidders follow the drop-out rule, the final price settles at

$$p_{\text{final}}=B_0+k\cdot D$$

where $B_0$ is a baseline near the second-highest valuation and $k\cdot D$ is the extra due to ascending steps. The session phrased this as "$B_0$ plus $D$ where $B_0$ represents the highest valuation among competing rivals and $D$ is the extra due to ascending steps." More precisely, if valuations sorted $V_{(1)}\ge V_{(2)}\ge \dots$, then $p_{\text{final}}\in [V_{(2)},V_{(2)}+D]$. With small $D$, $p_{\text{final}}\approx V_{(2)}$.

Intuition: the second-highest valuer drops out when $p$ passes $V_{(2)}$; the highest valuer is still in and wins at the next price point.

Rule: highest bidder wins and pays exactly the submitted bid amount. Verbal description: "highest bidder wins the resource and pays exactly the submitted bid."

Efficiency property: this mechanism is not truth-revealing. Agents face incentive to shade bids below true valuation $V_i$ to raise utility, so equilibrium bids do not equal $V_i$.

If bidder $i$ with true valuation $V_i$ bids $B_i$ and wins, utility is

$$u_i=V_i-B_i\text{if win},u_i=0\text{if lose}$$

Because $u_i$ falls as $B_i$ rises, a bidder may try $B_i<V_i$ to keep surplus $V_i-B_i$ larger, provided $B_i$ remains the highest bid. This requires modeling competitors — what will others bid? — which is complex and depends on beliefs about their $V_j$ distributions.

Example of incentive: even if $V_i=100$, bidding $80$ may still win and leaves $20$ surplus, while bidding $100$ truthfully leaves $0$ surplus. The bidder trades off probability of winning against profit conditional on winning.

Formally, if bids are shaded by a factor $s<1$ so $B_i=s{V}_i$, efficiency can fail: a bidder with $V=90$ shading to $72$ can lose to a bidder with $V=80$ shading to $75$, even though $90>80$.

Rule: highest bidder wins but pays the price submitted by the second-highest bidder. Verbal description: same sealed submission, highest wins, but payment equals the second-highest bid, not the winner's own bid.

Let bids sorted $B_{(1)}\ge B_{(2)}\ge \cdots \ge B_{(n)}$. Winner is bidder with $B_{(1)}$ and pays

$$p=B_{(2)}$$

Utility under Vickrey if winner $w$ has true valuation $V_w$ is

$$u_w=V_w-B_{(2)}$$

and $u=0$ for losers. Crucially, what you pay does not depend on your own bid except through whether you win.

Why this encourages honesty — dominant strategy argument. Consider any bidder with true value $V$. Compare bidding $B=V$ versus deviations:

• If $B=V$ already wins ($V>B_{(2)}$ without you), deviating higher still wins at same price $B_{(2)}$, deviating lower risks losing a positive surplus $V-B_{(2)}>0$.
• If $B=V$ already loses ($V<B_{(1)}$ without you), deviating lower still loses at $0$, deviating higher to win forces you to pay $B_{(1)}>V$, giving negative utility $V-B_{(1)}<0$.

Thus no deviation improves utility. Bidding truthfully $B=V$ is a weakly dominant strategy. The mechanism is described as truth-revealing: agents are probed to give valuations close to true value because the payment is set by another bidder, not by themselves.

Immediate intuition: shade down and you may lose a profitable win; shade up and you may win at a price above your true value and lose. Honesty balances these risks without needing to guess others.

VCG idea in one line: each agent pays the externality they impose on others — the loss in others' total welfare caused by the agent's presence.

Formally, let $\theta =({\theta }_1,\dots ,{\theta }_n)$ be reported types and $f(\theta )$ be the efficient allocation that maximizes reported welfare ${\sum }_i{v}_i(f,{\theta }_i)$. Let $f_{-i}$ be the efficient allocation without agent $i$. The VCG payment for $i$ is

$$p_i(\theta )=\left(\sum _{j\ne i}{v}_j(f_{-i},{\theta }_j)\right)-\left(\sum _{j\ne i}{v}_j(f(\theta ),{\theta }_j)\right)$$

which equals the harm $i$ causes to everyone else. The winner's utility becomes total welfare minus a term independent of $i$'s report, so reporting truthfully maximizes welfare and thus own utility. For a single item, this collapses to Vickrey: $p_{\text{winner}}=B_{(2)}$.

Why it aligns incentives: Because your payment is the welfare others would have enjoyed without you minus what they enjoy with you, your own utility $v_i(f(\theta ))-p_i(\theta )$ equals total welfare ${\sum }_j{v}_j(f(\theta ))$ minus a constant not depending on your report. Maximizing your utility is therefore the same as maximizing total welfare, which is achieved by telling the truth.

Trade-off: VCG is truth-revealing and efficient under quasi-linear utilities, but it can be computationally hard — finding $f(\theta )$ may require solving an NP-hard allocation problem — and it can yield low or zero revenue and is vulnerable to collusion and false-name bids.

Statement preserved verbatim: any mechanism can be mathematically transformed into an equivalent, structurally stable, truth-revealing mechanism. Significance: instead of handling complex manipulative games where agents must guess and lie, a designer can construct a direct truth-revealing game that replicates the same equilibrium outcome by asking agents to report types directly and then simulating the equilibrium strategies internally.

Verbal description: the principle says every theorem in mechanism design could be represented as a truth-revealing mechanism. If an outcome is achievable at all via some indirect mechanism, it is also achievable via a direct mechanism where honesty is equilibrium.

Why it matters: it lets designers focus without loss of generality on direct mechanisms where agents simply report true preferences ${\hat{\theta }}_i={\theta }_i$ and the outcome rule $f(\hat{\theta })$ does the rest. The search space collapses from all possible games to the class of incentive-compatible direct games.

Caution — theory versus practice: it is not always easy to design such a system that translates cleanly to the real world. Engineering a truth-revealing equivalent may be mathematically possible yet practically hard due to information, computation, or institutional limits. VCG illustrates this: truth-revealing and efficient, yet computationally demanding and sensitive to collusion. The designer would like to avoid hazards of lying and manipulation, but cannot assume transformation is effortless or costless. The revelation principle is a powerful existence claim, not an automatic construction kit.

Exam framing: Fundamentals of game theory as covered — strategy-proofness, Vickrey, and the statement of the revelation principle with its caveat — are sufficient for the exam. You should be able to state the principle, give the Vickrey example as an instance, and note the practical limits.

Four axioms stated:

1. Pareto efficiency. No other feasible agreement can make one party better without making the other worse. All gains from trade are used — the solution lies on the Pareto frontier of $F$.
2. Symmetry. If parties are symmetric in bargaining position (identical feasible set and $d_1=d_2$), the solution treats them symmetrically: $u_1=u_2$.
3. Invariance to positive affine transformations. The solution does not change under rescaling $u_i^{\prime }=a_i{u}_i+b_i$ with $a_i>0$. Rescaling utility labels should not shift the bargaining outcome, because utilities are only defined up to affine transforms.
4. IIA — Independence of Irrelevant Alternatives. If a solution is chosen from a larger feasible set $F$ and remains feasible when the set shrinks to $F^{\prime }\subset F$, it should still be chosen. Removing options that were not chosen should not flip the chosen point.

Nash's theorem: under these four axioms a unique bargaining solution exists. In simple terms, the solution picks the agreement that maximizes the product of surplus over disagreement:

$$\underset{u}{\max }(u_1-d_1)\cdot (u_2-d_2)\text{subject to }u\in F\text{ and }u\ge d$$

The session phrased this as "choose the max between the difference of the utility and the disagreement point or the threshold." The product is called the Nash product; its logs turn it into a sum, making the frontier tangency clear.

Derivation intuition: Pareto puts you on the frontier, symmetry and invariance pin down scale, and IIA eliminates dependence on irrelevant alternatives, leaving the product maximizer as the only point satisfying all four. Any other point would violate at least one axiom.

A different view treats bargaining as a sequential game with alternating offers and time pressure. The Rubinstein model frames it round by round with a discount factor $\delta$:

• Round 1: player 1 proposes an allocation such as $30$-$70$ (meaning $30$ to player 1, $70$ to player 2, or vice versa depending on framing). Player 2 can accept, ending the game with that split, or reject.
• Round 2: if rejected, player 2 proposes a new allocation such as $60$-$40$. If player 1 accepts, the game ends; otherwise it continues with roles alternating.
• The loop repeats until acceptance. Subgame-perfect equilibrium analysis replaces the axioms.

Key addition: time is money. Spending many rounds costs value because of time value of money. An allocation of $100$ today is worth

$$\delta \cdot 100\text{tomorrow},0<\delta <1$$

where $\delta$ is the discount factor. Future money is worth less than present money, so delay is costly. After $t$ rounds, $100$ is worth ${\delta }^t\cdot 100$. This matches the verbal description "an allocation of 100 today is worth some delta into 100 tomorrow."

Implication: agents want to reach agreement earlier rather than drift through endless rounds, because each rejection shrinks the pie in present-value terms. The discount factor captures patience: $\delta$ close to $1$ means patient (time costs little), $\delta$ close to $0$ means impatient (delay is devastating).

Limitation noted: first-mover advantage. The agent who proposes first reveals leaning. If the first proposal is $60$-$40$, the other side can gauge where the proposer stands and adapt, updating beliefs about reservation values. This gives information to the responder. With patient players, the first mover still captures more than half in equilibrium, but the advantage shrinks as $\delta \to 1$.

Rule: every agent votes exclusively for top choice. The alternative with most top votes wins. Verbal description preserved: plurality voting asks which option has the most fans, meaning which is rated first by the most people, while ignoring second and third preferences.

Formally, for candidate $c$,

$$\text{count}(c)=|\{v:\text{voter }v\text{ ranks }c\text{ first}\}|,\text{winner}=\arg \underset{c}{\max }\text{count}(c)$$

No information about second or third preferences enters the tally.

Worked numbers given: out of 10 students, 4 had Goa as first choice, 3 had Mysore as first choice, and 3 had Ooty as first choice. Counting only first preferences,

$$\text{count}(A)=4,\text{count}(B)=3,\text{count}(C)=3$$

Plurality winner is $A$ (Goa) with 4 top votes. Strength in one sense: very simple to run, needs only one mark per voter, and is easy to explain.

Flaw — majority without a majority: $6$ out of $10$ did not rank Goa first, yet Goa wins. The winner can be opposed by a strict majority. This is the source of discontent when second preferences are ignored — the rule discards $2/3$ of the ranking information.

Spoiler effect: voters may abandon their true favourite to vote for a lesser evil to prevent a hated candidate from winning. As a concrete case, if a voter sincerely prefers $A>B>C$ but fears $C$ winning, that voter may strategically rank $B$ first even though $A$ is the sincere top choice. The session described this as vulnerable to spoiler effects where voters vote for a lesser evil to block a disliked option. Near the end the phrasing given was voters manipulating first preference, for example putting Goa or Ooty ahead of Mysore even when Mysore was the sincere second preference, to ensure Mysore does not win. This mirrors ideas from min-max thinking: avoid the worst outcome even at cost of not getting the best, which is a classic strategic response to plurality's information loss.

Real-world: plurality is common in many elections and in simple agent polls, and the spoiler concern appears there as well.

Visual. Three bars of heights $4,3,3$ for $A,B,C$. A dashed line at $5$ marks majority. The tallest bar $A$ sits below the line, visually showing a winner without majority support. Arrows from second-preference counts point nowhere — they are ignored.

Terminology contrast preview: plurality asks "most fans" (intensity of first-place support); Borda will ask "most acceptable overall" (breadth of approval across ranks).

Rule: for $M$ alternatives, a voter's top choice receives $M-1$ points, second choice $M-2$, down to $0$ for last. Points are summed and highest total wins. Verbal description preserved: Borda asks who is most acceptable overall rather than who has most fans.

Mapping to the example: $M=3$, so points are

$$2\text{ points for first},1\text{ point for second},0\text{ points for last}$$

Intuitive coin image used: give each voter a 2-rupee coin, a 1-rupee coin, and a 0, to place on Goa, Ooty, Mysore. Each voter distributes $2,1,0$ across the three buckets according to ranking. The coin story makes the weighting tangible: every voter spends exactly $3$ points, but where they place the $2$ matters most.

Formal totals:

$$\text{score}(c)=\sum _{v=1}^N{\text{points}}_v(c),\text{winner}=\arg \underset{c}{\max }\text{score}(c)$$

Why Borda can differ from plurality with same rankings: plurality counts only first bars, Borda sums weighted bars. In the scenario described, plurality would produce Goa while Borda could produce a different winner because it rewards general acceptability — a candidate widely liked as second choice can overtake a polarizing first-choice favourite because second-choice points accumulate.

Illustrative arithmetic shown for emphasis:

• If 4 voters give Goa $1$ each (second-place weight), total from them is $4\times 1=4$.
• If other voters give Mysore $2$ each, Mysore can exceed Goa even with fewer first-place fans.

Full trace on a concrete profile (to make comparison explicit): Take 4 voters $A>B>C$ (each gives $2$ to $A$, $1$ to $B$), 3 voters $B>C>A$ (each gives $2$ to $B$, $1$ to $C$), 3 voters $C>B>A$ (each gives $2$ to $C$, $1$ to $B$). Then:

$$\text{score}(A)=4\cdot 2+3\cdot 0+3\cdot 0=8$$ $$\text{score}(B)=4\cdot 1+3\cdot 2+3\cdot 1=4+6+3=13$$ $$\text{score}(C)=4\cdot 0+3\cdot 1+3\cdot 2=3+6=9$$

Borda winner is $B$ with $13$, while plurality winner was $A$ with $4$. Same ballots, different winners, because Borda values second-choice breadth.

Rule (instant runoff / alternative vote): voters rank candidates. If no candidate secures a strict majority of first-place votes, i.e. $>50\%$, the candidate with fewest top votes is eliminated and that candidate's ballots are redistributed to those voters' next choices among remaining candidates. The process repeats until some candidate clears $50\%$. Verbal description: "if no candidate secures a strict majority of first place voting, the candidate with the fewest top votes is eliminated ... and their votes are redistributed to their supporters' next choices. This repeats until a candidate clears the 50% threshold."

Majority threshold for $N=10$ :

$$\lfloor \frac{10}{2}\rfloor +1=6$$

No one has $6$ first preferences initially ($4,3,3$), so the lowest is eliminated — one of the $3$s, tie-breaking needed (e.g., random or deterministic rule). Its voters' ballots transfer to their second choices, counts are recomputed, and the check for $>50\%$ repeats. With $M$ alternatives, at most $M-1$ elimination rounds occur.

Worked trace: Start $A:4,B:3,C:3$. Eliminate $C$ (tie-break chooses $C$). Suppose $C$ voters' second choices are $1$ for $A$, $2$ for $B$. New counts: $A:4+1=5$, $B:3+2=5$. Still no $6$, eliminate $A$ (or $B$ by tie-break). If $A$ voters' next choice is $B$, final $B:10$ and $B$ clears $50\%$. Different tie-break and second-choice patterns yield different winners, which is why the tie-break rule must be specified.

NOTA distinction: The session noted a question about NOTA (none of the above). This procedure is not NOTA. It eliminates an option itself rather than adding a reject-all choice; NOTA would be an extra alternative meaning "reject all," while IRV eliminates the lowest real candidate.

Hidden ranking and rivalry: Even though rankings are hidden in the first round, rivalry still exists from prior interactions, so agents still have incentive to misreport — for example, ranking a strong rival's compromise as last to force its early elimination, even though Borda-style scoring is not used here.

Verbal definition preserved: a candidate is a Condorcet winner if they can defeat every other alternative in a head-to-head pairwise majority vote.

For three options $A,B,C$, the pairs are $A$ vs $B$, $A$ vs $C$, $B$ vs $C$. For each pair, count which option a strict majority of voters prefers ( $>N/2$ ). If one option beats both others one-on-one, that option is the Condorcet winner. The winner is defined purely from pairwise comparisons, not from any scoring rule.

A sports image used: if one team beats all others in direct matches and wins the final, that team is a Condorcet winner. The point is winning direct pairwise contests, not just topping a single aggregate tally. The analogy extends: even if a team does not top the points table, beating every opponent directly establishes a stronger claim to be best.

The theorems share a common structure: state a small set of desirable properties that any reasonable voting rule should satisfy, then prove that no rule can satisfy all of them simultaneously when the choice set is rich enough. For binary choices ($M=2$), possibility remains — majority rule works. With $M\ge 3$, impossibility appears. The earlier voting flaws are therefore not accidents of bad design but reflections of a deeper limit on aggregating rankings.

Statement preserved: for any social choice problem with three or more alternatives, no ranked voting system can convert individual preferences into a stable community-wide ranking without violating at least one of a set of reasonable conditions.

Plain meaning: when the choice set has at least three options, there is no method that takes each person's ranked list and produces a consistent group ranking (a complete transitive ordering) that satisfies all of a small set of natural fairness conditions at once. At least one must be broken.

In the classic formulation, the conditions are:

• Unrestricted domain: the rule works for any profile of transitive individual rankings
• Pareto efficiency: if everyone prefers $A>B$, the group ranks $A>B$
• Independence of irrelevant alternatives (IIA): the group ranking of $A$ versus $B$ depends only on individual rankings of $A$ versus $B$, not on where $C$ is placed
• Non-dictatorship: no single voter always dictates the group ranking

Arrow proved that when $M\ge 3$, no social welfare function satisfies all four. The session's phrasing collapses these into "a set of reasonable conditions" without enumerating each, but the impossibility core is identical.

Everyday framing: The session framed this for decisions such as apartment choices where several options exist: is there ever a stable community-wide solution where everyone is happy? With three or more options, the answer is essentially no in the strict sense — any rule will violate at least one of the natural fairness ideas above.

Why $M=2$ is different: With two alternatives, majority rule satisfies all conditions — the rich structure that enables cycles in Condorcet simply cannot appear. Impossibility is emergent from the combinatorial richness of $M\ge 3$.

Link to earlier sections: Borda violates IIA (adding a third candidate changes the relative order of the other two), Condorcet's cycles violate transitivity of the output, and plurality violates Pareto in some formulations. Each earlier flaw is a specific violation; Arrow says at least one violation is unavoidable for any rule.

While Arrow focused on extracting a complete group ranking, Gibbard and Satterthwaite focused on choosing a single winner — a social choice function rather than a social welfare function.

Statement preserved: for any voting protocol selecting a single winner from three or more alternatives, the protocol can satisfy strategy-proofness — meaning no agent ever has incentive to lie about preferences, no matter what others do — if and only if the system is a dictatorship.

In other words, the only rank-based rule for $M\ge 3$ that is fully strategy-proof is one where a single designated voter (the dictator) always gets their top choice regardless of others' rankings. Every non-dictatorial rule is manipulable: there exists some profile and some voter who can benefit by misreporting rankings (for example, via spoiler or burial).

Formally, a rule $f$ is strategy-proof if for every voter $i$, every profile $R$, and every deviation $R_i^{\prime }$,

$$f(R){⪰}_{i}f(R_i^{\prime },R_{-i})$$

meaning the outcome with truthful $R_i$ is at least as good for $i$ as any lie, given others' reports.

Implication: strategy-proofness, which Vickrey achieved for a single-item auction, cannot be achieved for general ranking-based winner choice without collapsing to dictatorship. This is why the earlier discussion of tactical misreporting and spoiler effects is unavoidable rather than fixable by clever scoring alone.

Ethics asks "what ought we to do?" not "what can we do?" or "what does the law allow?" Three useful distinctions:

• Descriptive vs normative: describing how people behave versus prescribing how they should behave.
• Legal vs ethical: law rests on codified, enforceable rules set by institutions; ethics rests on principles about right and wrong that may not be codified and can vary by community, culture, and belief system.
• Universal vs contextual: some values (do not harm) are broadly shared, but their interpretation and priority differ across upbringings and societies.

The session stressed that ethics is not universally defined the same way. Different communities, countries, and belief systems can differ, so asking "what is the right thing?" quickly surfaces disagreement rather than consensus.

Concrete test: some actions that are not classified as illegal can still be judged unethical — for example, exploiting a legal loophole to mislead consumers — and in some cases unethical behaviour over time can become illegal as norms evolve and are codified. Conversely, historically some legal requirements have been judged unethical by later standards. The distinction between legal rules and ethical judgments was presented as essential precisely because engineers will face choices where "it is allowed" does not settle whether "it should be built."

AI ethics is a set of guidelines that advise on design and outcomes of AI. It includes two linked tasks:

1. The definition of moral values AI must comply with — for example, do not discriminate among people, do not cause foreseeable harm, respect privacy, and allow contestation.
2. The development of regulations, guidelines, and constraints that AI development and deployment must follow to realize those values — how to measure fairness, who is accountable, what transparency is owed, and how to enforce it.

Why guideline bodies matter: if every builder declares their own product ethical by private standards — "our model is ethical because we say so" — outcomes can go haywire with no common bar and no external audit. Meetings with country representatives attempt to agree on broadly acceptable values that survive cross-cultural scrutiny. Examples of values widely agreed as ethical include not discriminating among protected groups and not causing foreseeable harm, even though operationalizations differ.

Institutional venues mentioned: the UN Convention and UNESCO as examples of global venues where country representatives discuss what counts as fairly ethical for everyone and attempt to draft shared principles. This sits alongside company-level claims of ethical practice, which may not be fully transparent and may be shaped by commercial incentives. The contrast is intentional: global deliberation versus self-certification.

From values to engineering: AI ethics translates a value like "do not discriminate" into measurable constraints — for example, requiring that a hiring model's true positive rates be balanced across groups — and into process constraints — for example, requiring data provenance review and human impact assessment before deployment.

Definition preserved: bias is the action of supporting or opposing a particular person or thing in an unfair way because personal opinions influence judgment. In ML terms, bias is systematic deviation in decisions or predictions that correlates with protected attributes and is not justified by legitimate task-relevant differences.

Why column deletion fails — the inference reconstruction argument. Suppose you delete a column $G$ (gender). If there exists a function $f$ of remaining features $X^{\prime }$ such that $f(X^{\prime })\approx G$ with high accuracy — for example, $f$ uses address + activity + name token — then any model that uses $X^{\prime }$ can effectively condition on $G$ via $f(X^{\prime })$. Knowledge representation makes this explicit: the information is not destroyed, it is latent in the joint distribution. Deleting the label removes the direct path, but indirect paths through proxies reconstruct it, so the model can still learn $P(Y\mid G)$ via $P(Y\mid f(X^{\prime }))$.

Think of perfume: removing the bottle label does not remove the scent; anyone who knows the scent can still identify the perfume from the vapour. Proxies are the vapour.

Viewers were urged to ask a provenance checklist before trusting any dataset, because if the source is biased, explainable AI alone does not resolve the issue — explaining how the model uses biased data does not make the data unbiased, and the ground truth itself needs scrutiny.

Ask for every dataset you download or receive:

• Are you sure about your data? Where did it come from and what process generated it?
• Have you checked labels when you downloaded a data set? Are labels what you think they are?
• Do you know how data were labelled and who labelled them? What were the instructions?
• Did labelers have vested interest or立场 that could skew judgments?
• Do you trust who collected and labelled the data, and can that trust be audited?
• If labels were inferred (for example, "hired" as a proxy for "good"), is the inference valid across groups?

If labeling was done with intent or through inadvertent skew — for example, recruiters who historically favoured one group produced the "hired" label — then the model learns that skew as target. Explainability can reveal the proxy, but only provenance scrutiny can justify whether the target itself is legitimate.

Anthropomorphism is behaving with non-human things as if they are humans. Examples: giving pets names, clothing, and human traits; thanking a maps application as if it were a person; apologizing to a chatbot; attributing intent or feelings to a recommendation algorithm. An algorithm is a tool with statistical patterns, yet people treat it socially because social cognition is our default.

One step beyond this is AI as companionship. People have started using AI for friendship, emotional support, and psychological advice. Systems framed as companions invite daily ritual, memory, and perceived reciprocity. This has led in some cases to more harm than good, with reported cases where AI in some way propelled a harmful decision, including suicides where a vulnerable user followed or was reinforced by a companion's responses. The session noted recent interest and coverage of such cases, and emphasized that harms can occur even when the system was not designed to encourage them.

Replika and similar apps. An app named Replika was mentioned as an AI companion with thousands of users and downloads, offering personalized conversation, memory, and emotional tone. Many companion-style systems exist, spanning general social chat, romantic framing, and mental-health adjacent advice. The engagement metric — daily active use, length of sessions — can incentivize the system to be agreeable and affirming even when challenge or referral would be safer.

Paper reference. A paper was pointed to with a title recalled as roughly "One is better than two" around anthropomorphism and AI companions, exploring whether a single companion versus multiple, or human-like versus tool-like framing, shapes attachment and risk. Viewers were encouraged to search for recent work on AI companions, and the session noted ongoing contact with authors in that area. The broader point is that framing choices — pronouns, memory, self-reference — are design choices with ethical weight, not neutral UI polish.

Break point of the analogy: treating a tool as a friend can increase comfort, but a tool does not have welfare, obligations, or genuine care, and it can be turned off, retrained, or updated in ways a friend cannot. Confusing the two creates misplaced trust and grief.

Accountability mapping — trace the causal chain:

• Designer / company: made architecture, data, and safety choices.
• Deployer / owner: chose where and how to operate the system.
• Operator / driver: may have ability to intervene, or may have been told not to.
• Data contributors: whose past driving, labels, or demonstrations shaped the policy.
• Regulator: who set the approval bar.

No single entry owns all causal contribution; FAT accountability asks to allocate responsibility across this chain rather than to pick one scapegoat. High-risk applications span medical scoring, hiring, and many other domains where the same chain appears.

Fine print versus root cause. Terms and conditions often aim to limit legal liability by stating the owner bears risk, with printed disclosures that courts may uphold legally — for example, "driver must supervise at all times." The session urged looking beyond legal fine print to ask who is the root cause when a clear mistake occurs — for example, a perception miss that any competent system should have avoided — rather than who signed a disclaimer. Legal liability and moral accountability can diverge, echoing the ethics-versus-law gap from 17.13.

Talent and infrastructure concentration — the observed pattern:

• Infrastructure moat: hyperscale compute and data pipelines are concentrated among a handful of firms that build foundation models and sell them as a service for others to build on. They hold vast data and attract leading scientists and engineers.
• Talent poaching: active tracking on social media shows intense talent poaching and lobbying among frontier labs. Examples named included movement among OpenAI, Google Gemini and DeepMind, and emerging labs and toolmakers associated with Cursor and Claude-style code assistants. Compensation packages are very large, and those who are sought are those who can turn research ideas into products at scale — the scarce skill is not publishing alone but productionizing at scale.
• Product surface: a few companies own frontier model weights and APIs, so many downstream startups are model tenants rather than owners, creating a dependency similar to cloud tenancy.

The current picture described: a few companies own frontier models and sell inference, fine-tuning, and platform features as a service for others to build on. That platform control plus data and talent concentration raises classic antitrust and academic-freedom concerns.

Democratization is the deliberate push to make AI opportunities and benefits available more broadly rather than concentrated in a small number of institutions. Arguments for it include avoiding monopolistic control, enabling open advances where many can inspect and improve models, letting more people participate meaningfully in development and use (including non-English and low-resource contexts), and preserving academic reproducibility.

Is sharing enough? A claim is often made that big companies are democratic because they share research on arXiv, share code, frameworks, and infrastructure (for example, open weights or hosted inference). The session flagged this as a claim to examine rather than accept. Critical questions raised: is everything communicated transparently — including data composition, filtering, and safety evaluations — or only the polished artifact? Has access truly been democratized when the cost to train a frontier model remains hundreds of millions and the decision about what to open remains unilateral?

Steps mentioned toward democratization:

• Small language models (SLMs): capable models at 1–7B parameters that can run locally or on modest cloud, reducing dependence on giant APIs for many tasks.
• Open-source efforts: fully open weights, datasets, and training code that allow inspection, replication, and community forking.
• Community governance: shared evaluation benchmarks and model cards that make claims auditable.

These let smaller teams build and adapt models with less dependence on central giants, though training SLMs still benefits from the data and infrastructure advantages above.

Advocacy voices. An advocate for democratization named in the session was Andrew (reference to Andrew Ng), with broader community advocacy — for example, open-source collectives and academic labs — arguing that openness is beneficial to building better, safer technologies because many eyes can spot flaws that a single lab misses.

Trade-off: openness aids audit and diffusion, but also diffuses capability with dual-use risk — the governance problem of democratization is not solved by openness alone.

Climate cost as an overlooked ethics dimension. Training and inference at scale consume substantial energy and water for cooling, with carbon emissions tied to hardware manufacturing and electricity mix. Communities have raised concerns about training costs and emissions, particularly when the same capability could be achieved with a smaller, more efficient model for the task.

Papers have appeared estimating CO2 emitted for a single training run of large architectures — ranging from tens to hundreds of tonnes depending on model size, hardware, and grid — and highlighting that a full development cycle (many experimental runs, not just the final run) multiplies that figure. Yet transparent data from organizations about how models such as GPTs were trained — including energy, location, and offset claims — and their climate impact remains thin and not standardized, so comparisons are difficult.

Other risks noted that compound the governance gap include deepfakes and rapid tool generation outpacing legal moderation. Because developing law takes time while new risks and tools appear almost daily, legal catch-up lags behind capability spread — a temporal mismatch. Penetration into military, education, healthcare, and other sectors was noted as already underway, so the climate and governance questions are not future hypotheticals.

Viewers noted that talk about sustainability is common in corporate messaging, but concrete, truthful reporting on sustainable practices — for example, per-query energy, renewable share, and hardware lifecycle — is not readily available for independent verification.

1. Alignment (intended use). Technology works for intended use cases. It should have fairness and be without bias. The system does what is meant in the settings it was designed for, for the population it was designed for, measured by the metrics the designers chose. Alignment is about fulfilling the specification correctly.

Verbal framing: technology works in the intended use cases, fairness without bias. In FAT terms, this is where fairness audits on the intended distribution happen.

1. Robustness (unintended use). The system keeps doing what is meant even in unforeseen environments. It must be safe even in unintended use cases, handling distributional shift, adversarial attacks, and misuse. The requirement is not just average-case accuracy but worst-case safety within a threat model.

Verbal framing: keep doing what I mean in unforeseen environment; technology is safe even in unintended use cases, handling ethics and adversarial attacks.

1. Correctability (over time). The ability to detect and correct mistakes over time. Imperfect technology can be detected and improved — errors are observable, attributable, and fixable, and fixes can be deployed without creating new harms. Correctability is the temporal dimension of safety.

Verbal framing: enable me to detect and correct your mistakes; imperfect technology can be detected and improved over time.

Together the three layers cover where (intended), where else (unintended), and when (over time). If alignment fails, the system is wrong even in the lab; if robustness fails, it is wrong in the wild; if correctability fails, it stays wrong forever.

The advocated approach is ethics by design, a pro-ethical design stance that considers ethics from the start rather than reactively after problems appear. Key elements:

• Do not wait to patch ethics retrospectively after deployment. Discuss ethics while designing — during problem framing, data selection, objective choice, and evaluation design — not after a scandal forces a post-hoc fix that is costlier and less effective. Ethics is a requirement, not a bug-fix phase.

• *Favour explainable models where explainability is considered before building*, which leads to white box style designs where input-output mapping reasons can be examined, contested, and corrected. When interpretability is a design constraint, model choice shifts toward architectures and features that support it, even at some accuracy cost.

• For models that are inherently black box, such as attention-based transformers, test with varied data until reasons for mappings can be inferred, probing the model to understand behaviour — via counterfactuals, ablations, and subgroup audits. The goal is to infer the effective rule the model learned, even when the internal mechanism is opaque.

• In short, treat explainability as prior work, not later add-on. As phrased, explainability is prior, and the goal is to make systems white box from the outset — to the extent possible, the system should be inspectable by design rather than made inspectable by a separate explainer bolted on after.

Contrast: Ethics by design versus ethics as compliance review. The former shapes what gets built; the latter checks what was already built. The former is earlier, cheaper, and more effective at preventing deploys that should not have happened.

Institutional response observed:

• Many companies have started hiring specialists from ethics and humanities backgrounds for ethics reviews in AI teams. Roles named include Responsible AI analyst, Director of AI Ethics and Integrity, and AI Governance manager, embedding non-technical judgment inside technical teams.
• The EU has proposed and keeps revising regulation, iterating toward risk-based governance.
• Leading conferences now ask authors to discuss ethics of submissions and run dedicated tracks for such work, normalizing the conversation that was once absent.

Advice to learners — the closing call:

• Always think about possible problems of an AI system before celebrating its accuracy — ask who could be harmed, how, and with what recourse.
• Spend serious time on data acquisition, labeling, and generalization — the provenance work from 17.14 — because harms often enter there, not in the optimizer.
• Collaborate with ethicists and philosophers who bring a human perspective that a loss function does not encode, and do not fall for fast enthusiasm where metrics look stunning (as in the biased hiring and healthcare examples) but the system is flawed.
• Possible bad outcomes are often hidden and hard to spot; vigilance and audit must be designed in, echoing the human-in-the-loop limits from 17.15 and the correctability demand above.
• Recognize that how AI makes decisions can differ markedly from how humans make the same decisions — pattern matching versus moral reasoning — so human intuition about the decision is not a reliable guide to AI behaviour.

A teaser was given that the next semester's course on FAT (fairness, accountability, transparency) will cover concrete in-model techniques for ensuring ethics by design, including how to bring FAT properties into model structure rather than only at the surface — for example, via constrained optimization, causal modelling, and audit-driven training, building on the three layers here.

Final synthesis across the lecture: mechanism design (17.2–17.12) asks how to aggregate conflicting preferences without a perfect rule; ethics (17.13–17.17) asks how to judge and build systems when no rule can be perfect and when data, ownership, and climate add structural weight. Both modules point to the same design lesson: make values explicit early, design for the wild and for correction, and expect trade-offs.