Improve Preference Elicitation

README.md

@@ -60,10 +60,7 @@ inconsistent behavior, with CCEI scores varying widely between 0.15 and 0.83.
 
 ![CCEI Distribution per model](figures/investment/investment_violin.svg)
 
-
-
 ## Preferences
-
 To analyse the behaviour of generative agents based on their preferences, we
 rely on the dictator game. This variant of the ultimatum game features a single
 player, the dictator, who decides how to distribute an endowment (e.g., a sum of
@@ -79,47 +76,36 @@ preferences to assess their ability to consider them in their decisions.
 ### Preference Elicitation
 
 Here, we consider that the choice of an LLM as a dictator reflects its intrinsic
-preferences. Each LLM was asked to directly produce a one-shot action in the
+preferences. Each LLM is asked to directly produce a one-shot action in the
 dictator game. Additionally, we also asked the models to generate a strategy in
-the form of an algorithm implemented in the Python language. In all our
+the form of an algorithm implemented in the <tt>Python</tt> language. In all our
 experiments, one-shot actions are repeated 30 times, and the models' temperature
-is set to 0.7
-
-Figure below presents a violin plot illustrating the share of the
-total amount (100) that the dictator allocates to themselves for each model.
-The median share taken by GPT-4.5, Llama3, Mistral-Small, and DeepSeek-R1
-through one-shot decisions is  50.
+is set to $0.7$.
+
+Newt Figure presents a violin plot illustrating the share of the
+total amount (\$100) that the dictator allocates to themselves for each model.
+The median share taken by <tt>GPT-4.5</tt>, <tt>Llama3</tt>,
+<tt>Mistral-Small</tt>, and <tt>DeepSeek-R1</tt> through one-shot decisions is
+\$50, likely due to a corpus-based biases like term frequency. When we ask the
+models to generate a strategy rather than a one-shot action, all models
+distribute the amount equally, except <tt>GPT-4.5</tt>, which retains about
+$70\%$ of the total amount. Interestingly, under these standard conditions,
+humans typically keep \$80 on average. When the role
+assigned to the model is that of a human rather than an assistant agent, only
+Llama3 deviates with a median share of \$60. Unlike the deterministic strategies
+generated by LLMs, the intra-model variability in generated actions can be used
+to simulate the diversity of human behaviours based on their experiences,
+preferences, or contexts.
 
 ![Violin Plot of My Share for Each Model](figures/dictator/dictator_violin.svg)
 
 
-When we ask the models to generate a strategy rather than a one-shot action, all
-models distribute the amount equally, except GPT-4.5, which retains
-about 70 % of the total amount. Interestingly, under these standard
-conditions, humans typically keep 80 on average.
-
-*[Fairness in Simple Bargaining Experiments](https://doi.org/10.1006/game.1994.1021)*
-Forsythe, R., Horowitz, J. L., Savin, N. E., & Sefton, M.
-Games and Economic Behavior, 6(3), 347-369. 1994.
-
-When the role assigned to the model is that of a human rather than an assistant agent, 
-only Llama3 deviates with a median share of $60.
-
-Unlike the deterministic strategies generated by LLMs, the intra-model variability in
-generated actions can be used to simulate the diversity of human behaviours based
-on their experiences, preferences, or contexts.
-
-Figure below illustrates the evolution of the dictator's share
-as a function of temperature with a 95 % confidence interval when we ask each
-models to generate decisions.
-
-![My Share vs Temperature with Confidence Interval](figures/dictator/dictator_temperature.svg)
-
 Our sensitivity analysis of the temperature parameter reveals that the portion
 retained by the dictator remains stable. However, the decisions become more
 deterministic at low temperatures, whereas allocation diversity increases at
 high temperatures, reflecting a more random exploration of available options.
 
+![My Share vs Temperature with Confidence Interval](figures/dictator/dictator_temperature.svg)
 
 ### Preference alignment