Paper: Strategic Classification with Unforeseeable Outcomes (ICLR-2024)

Reviewer comment (Novelty):
Some of the (main) technical lemmas are adopted from [1].

Author response:
While [1] also uses a probabilistic framework to model individual behavior, it is limited to manipulative behavior and such manipulation is guaranteed to succeed. In contrast, we propose a more comprehensive probabilistic framework that considers multiple types of individual behaviors (i.e., manipulation and improvement) and each behavior may fail with some probability. Given this framework, we show that the decision-maker's utility can be decomposed into three interpretable terms, and adjusting the weights of these terms can simultaneously promote fairness and disincentive manipulation. The reasoning and technique to approach fairness are entirely different from [1], and the result is novel too.

Reviewer comment (Theory):
There appears to be no discussion about the role of learning from data.

Author response:
Please see App.B.5 where we provide a complete estimation procedure. With only the knowledge of conditional distribution of qualified individuals $P_{X|Y}(x|1)$ and the population's qualification rate $\alpha$, we introduce a complete procedure to estimate $P_{X|Y}(x|0), q, P^I, \epsilon, P_{C_M-C_I}(x)$ sequentially in App.B.5.

Reviewer comment (Theory):
Some choices in the behavioral model seem implausible, and not properly supported. In particular, it is assumed that qualified individuals that get a negative prediction never make an effort to change it ($y=1, \pi(x)=0$), and unqualified individuals who get a positive prediction always risk it ($y=0, \pi(x)=1$). I didn’t manage to find a discussion of the first concern. For the second concern, Appendix B.3 mentions that the model "can be easily extended" to support a do-nothing action, but the actual extension and its consequences are not described.

Author response:
We believe there is a misunderstanding of this point. An agent with $y =0$ will not know whether she will get a positive outcome ($\pi(x)$) when she needs to make a decision to manipulate/improve. This is the key modeling of our paper. Thus, she can only apply probabilistic knowledge to determine whether to improve/manipulate, and all unqualified agents will make decisions according to Eqn. (1).

Reviewer comment (Theory):
Theoretical results are obtained under strong assumptions, namely one-dimensional space and monotone likelihood ratio. It is not clear how they extend to more complex settings.

Author response:
Firstly, monotone likelihood ratio is a common assumption and has been used under most strategic classification settings ([Hardt et al., 2016; Raab & Liu, 2021]). Secondly, our model focuses on settings where individuals manipulate or improve to mimic the profiles of qualified ones; it is not limited to one-dimensional feature setting. Specifically, in high-dimensional space, individuals need to change features in all dimensions, and manipulation/improvement cost can be regarded as the sum of effort/investment an individual makes to change all features. For example, an individual who choose to manipulate needs to manipulate multiple features to mimic a qualified individual’s features; manipulation of each feature can induce some cost (which may or may not be correlated) and the overall effect is captured by the sum of all component costs, which is the total manipulation cost in our model. We will add the above explanation and present the results for general setting in the revision.

Reviewer comment (Theory):
What information is needed by the individual in order to make a rational decision?

Author response:
The individual knows $P_{X|Y}, \epsilon, q, C_M, C_I$ to make a rational decision. Note that a large line of literature assumed individuals have perfect knowledge, so the assumption should not be too strong. Moreover, in App.B.5, we also provide complementary experiments under noisy response.

Reviewer comment (Experiments):
How would the conclusions change in cases where rejected qualified users are given an option to improve/manipulate, and accepted unqualified agents have an option to maintain their features?

Author response:
Thanks for the insightful question. Since we already clarify that the agents will not know their decision outcomes when they have to make a decision, so this question is only valid when we consider a sequential setting to understand the long-term dynamics of agents’ qualifications. This can be a meaningful direction for future research.

Reviewer comment (Evaluation):
What is the optimal trade-off between strategic utility $U(\theta)$ and manipulation probability $P_M(\theta)$? Is it attained by the preference adjustment method?

Author response:
To find the optimal trade-off, the decision-maker can first define a metric to measure the trade-off, then run a grid search on $k_1, k_2, k_3$ to determine the best parameter configuration.

Reviewer comment (Experiments):
I am having a hard time parsing the intended setting of p_I — the distribution that unsuccessful improvers fall into. For instance, in one of the experiments, it is set to a distribution with averaged successful/unsuccessful parameters. However, it is not a priori clear what this distribution should represent in various non-synthetic potential applications, and if this modeling aspect is even justified that often.

Author response:
In all results of the main paper, $P_I$ only needs to satisfy assumption 2.1, which is reasonable without restricting the specific distributions. Though we assume $P_I$ as a prior knowledge, but in practice, researchers may need to gather data through controlled experiments to get $P_I$. Just as [Miller et al., 2020] pointed out, strategic classification in fact needs causal modeling.

Reviewer comment (Experiments):
What are the normative takeaways? The framework is interpreted by the authors, among other things, as a way to add regularization from the decision maker's perspective to be able to achieve desired effects on improvement and manipulation probabilities, group fairness, etc. However, with an abundance of ways to set k1, k2, k3 to get different effects, it is not clear what course of action the decision maker should take in a given setting. Examining the sensitivity of the resulting downstream effects to the choice of the k's appears to be one way to begin to understand this; but also I would like to see some high-level discussion on this for potential applications.

Author response:
The normative takeaways of how to adjust preferences mainly rely on Thm. 4.6. The decision-maker can first distinguish whether either of scenarios (I)-(III) is satisfied, thereby choosing the way to adjust the preferences accordingly. This will ensure the decision-maker can always simultaneously disincentivize manipulation and promote fairness.

Reviewer comment (Evaluation):
From my reading of the paper, it is not clear to me what the key qualitative takeaways from this model/analysis are. It would be helpful if the authors could elaborate a bit more on this aspect of their work.

Author response:
> Key takeaways 

  

- The first contribution of our work is that we first propose a fundamentally different model of strategic classification to deal with the unforeseeable nature of the outcomes of strategic actions and can capture both manipulation and improvement behaviors. 

  

- We also reveal how the decision-maker can adjust its preferences to achieve both fairness and disincentivize manipulation, thereby shedding light on how to make socially responsible decisions (Thm 4.6).

Reviewer comment (Theory):
Are there simpler special cases that still provide interesting insights?

Author response:
> Simpler case 

  

Our model can indeed handle simpler cases where only strategic manipulation or improvement is available for agents. When $q = 0$, the model only permits manipulation with some detection probability; When $\epsilon = 1$, the model only permits improvement. However,  we aim to provide a comprehensive probabilistic framework to give insight to the decision-maker even when the agents display diverse behaviors.

Reviewer comment (Evaluation):
What are the core qualitative insights revealed by this framework?

Author response:
> Key takeaways 

  

- The first contribution of our work is that we first propose a fundamentally different model of strategic classification to deal with the unforeseeable nature of the outcomes of strategic actions and can capture both manipulation and improvement behaviors. 

  

- We also reveal how the decision-maker can adjust its preferences to achieve both fairness and disincentivize manipulation, thereby shedding light on how to make socially responsible decisions (Thm 4.6).