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update and verify charts one more time
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dev/poster/poster.pptx

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dev/poster/www/logo-repo.png

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dev/poster/www/logo_appendix.png

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dev/poster/~$poster.pptx

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paper/sections/introduction.rmd

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Figure \@ref(fig:poc) illustrates this idea for a binary problem involving a linear classifier and the counterfactual generator proposed by Wachter et al. @wachter2017counterfactual: the implementation of AR for a subset of individuals immediately leads to a visible domain shift in the (orange) target class (b), which in turn triggers a model shift (c). As this game of implementing AR and updating the classifier is repeated, the decision boundary moves away from training samples that were originally in the target class (d). We refer to these types of dynamics as **endogenous** because they are induced by the implementation of recourse itself. The term **macrodynamics** is borrowed from the economics literature and used to describe processes involving whole groups or societies.
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```{r poc, fig.cap="Dynamics in Algorithmic Recourse: (a) we have a simple linear classifier trained for binary classification where samples from the negative class ($y=0$) are marked in blue and samples of the positive class ($y=1$) are marked in orange; (b) the implementation of AR for a random subset of individuals leads to a noticable domain shift; (c) as the classifier is retrained we observe a corresponding model shift; (d) as this process is repeated, the decision boundary moves away from the target class."}
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```{r poc, fig.cap="Dynamics in Algorithmic Recourse: (a) we have a simple linear classifier trained for binary classification where samples from the negative class ($y=0$) are marked in orange and samples of the positive class ($y=1$) are marked in blue; (b) the implementation of AR for a random subset of individuals leads to a noticeable domain shift; (c) as the classifier is retrained we observe a corresponding model shift; (d) as this process is repeated, the decision boundary moves away from the target class."}
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knitr::include_graphics("www/poc.png")
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```
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We think that these types of endogenous dynamics may be problematic and deserve our attention. From a purely technical perspective we note the following: firstly, model shifts may inadvertently change classification outcomes for individuals who never received and implemented recourse. Secondly, we observe in Figure \@ref(fig:poc) that as the decision boundary moves in the direction of the non-target class, counterfactual paths become shorter. We think that in some practical applications, this can be expected to generate costs for involved stakeholders. To follow our argument, consider the following two examples:
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We think that these types of endogenous dynamics may be problematic and deserve our attention. From a purely technical perspective, we note the following: firstly, model shifts may inadvertently change classification outcomes for individuals who never received and implemented recourse. Secondly, we observe in Figure \@ref(fig:poc) that as the decision boundary moves in the direction of the non-target class, counterfactual paths become shorter. We think that in some practical applications, this can be expected to generate costs for involved stakeholders. To follow our argument, consider the following two examples:
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::: {.example #consumer name="Consumer Credit"}
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Suppose Figure \@ref(fig:poc) relates to an automated decision-making system used by a retail bank to evaluate credit applicants with respect to their creditworthiness. Assume that the two features are meaningful in the sense that creditworthiness increases in the south-east direction. Then we can think of the outcome in panel (d) as representing a situation where the bank supplies credit to more borrowers (orange), but these borrowers are on average less creditworthy and more of them can be expected to default on their loan. This represents a cost to the retail bank.
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Suppose Figure \@ref(fig:poc) relates to an automated decision-making system used by a retail bank to evaluate credit applicants with respect to their creditworthiness. Assume that the two features are meaningful in the sense that creditworthiness increases in the South-East direction. Then we can think of the outcome in panel (d) as representing a situation where the bank supplies credit to more borrowers (orange), but these borrowers are on average less creditworthy and more of them can be expected to default on their loan. This represents a cost to the retail bank.
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::: {.example #student name="Student Admission"}
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Suppose Figure \@ref(fig:poc) relates to an automated decision-making system used by a university in its student admission process. Assume that the two features are meaningful in the sense that the likelihood of students completing their degree increases in the south-east direction. Then we can think of the outcome in panel (b) as representing a situation where more students are admitted to university (orange), but they are more likely to fail their degree than students that were admitted in previous years. The university admission committee catches on to this and suspends its efforts to offer Algorithmic Recourse. This represents an opportunity cost to future student applicants, that may have derived utility from being offered recourse.
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Suppose Figure \@ref(fig:poc) relates to an automated decision-making system used by a university in its student admission process. Assume that the two features are meaningful in the sense that the likelihood of students completing their degree increases in the South-East direction. Then we can think of the outcome in panel (b) as representing a situation where more students are admitted to university (orange), but they are more likely to fail their degree than students that were admitted in previous years. The university admission committee catches on to this and suspends its efforts to offer Algorithmic Recourse. This represents an opportunity cost to future student applicants, that may have derived utility from being offered recourse.
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:::
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Both examples are exaggerated simplifications of potential real-world scenarios, but they serve to illustrate the point that recourse for one single individual may exert negative externalities on other individuals.

paper/sections/mitigation.rmd

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plts = vcat(plts..., plt)
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end
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plt = plot(plts..., size=(750,200), layout=(1,4))
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savefi\text{extcost}(plt, "dev/paper/www/mitigation.png")
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savefig(plt, "paper/www/mitigation.png")
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```
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