In an era where language models are increasingly integrated into decision-making and communication, understanding the biases within Large Language Models (LLMs) becomes imperative, especially when these models are applied in the economic and political domains. This work investigates the impact of fine-tuning and data selection on economic and political biases in LLMs. In this context, we introduce PoliTune, a fine-tuning methodology to explore the systematic aspects of aligning LLMs with specific ideologies, mindful of the biases that arise from their extensive training on diverse datasets. Distinct from earlier efforts that either focus on smaller models or entail resource-intensive pre-training, PoliTune employs Parameter-Efficient Fine-Tuning (PEFT) techniques, which allow for the alignment of LLMs with targeted ideologies by modifying a small subset of parameters. We introduce a systematic method for using the open-source LLM Llama3-70B for dataset selection, annotation, and synthesizing a preferences dataset for Direct Preference Optimization (DPO) to align the model with a given political ideology. We assess the effectiveness of PoliTune through both quantitative and qualitative evaluations of aligning open-source LLMs (Llama3-8B and Mistral-7B) to different ideologies. Our work analyzes the potential of embedding specific biases into LLMs and contributes to the dialogue on the ethical application of AI, highlighting the importance of deploying AI in a manner that aligns with societal values.

Crowdfunding is quickly emerging as an alternative to traditional methods of funding new products. In a crowdfunding campaign, a seller solicits financial contributions from a crowd, usually in the form of pre-buying an unrealized product, and commits to producing the product if the total amount pledged is above a certain threshold. We provide a model of crowdfunding in which consumers arrive sequentially and make decisions about whether to pledge or not. Pledging is not costless, and hence consumers would prefer not to pledge if they think the campaign will not succeed. This can lead to cascades where a campaign fails to raise the required amount even though there are enough consumers who want the product. The paper introduces a novel stochastic process --- anticipating random walks --- to analyze this problem. The analysis helps explain why some campaigns fail and some do not, and provides guidelines about how sellers should design their campaigns in order to maximize their chances of success. More broadly, Anticipating Random Walks can also find application in settings where agents make decisions sequentially and these decisions are not just affected by past actions of others, but also by how they will impact the decisions of future actors as well.

Crowd innovation is an emerging technology where innovation is sourced out to the public through an open call. At the center of crowd innovation is a resource allocation problem: there is an abundance of workers but a scarcity of high skills, and an easy task assigned to a skilled worker is a waste of resources. This problem is complicated by the fact that the exact difficulties of innovation tasks may not be known in advance, so tasks that require high-skill labor cannot be identified and allocated ahead of time. More problematically, worker skills in a crowd environment are their own private information, and they may have an incentive to misrepresent that information. Taken together, these aspects imply that the firm has to solve the challenging problem of how to assign tasks to workers even though it knows neither the difficulties of the tasks nor the skills of the workers. We first relax the constraint that the firm does not know the skills of the workers (and that workers participate voluntarily) and examine the resulting assignment problem. We show that the solution to this problem takes the form of a skill hierarchy, where tasks are first attempted by low-skill labor, and high-skill workers only engage with a task if less skilled workers are unable to finish it. We derive this structure of the optimal matching by studying a dynamic programming formulation. The most distinctive property of the optimal matching is that it ensures that the heterogeneous skills of the available workers are efficiently utilized.

Innovation contests have emerged as a viable alternative to the standard research and development process. They are particularly suited for settings that feature a high degree of uncertainty regarding the actual feasibility of the end goal. The objective of the contest designer is to maximize the probability of reaching the innovation goal while minimizing the time it takes to complete the project. Obviously here the important question is how to best design these contests. This paper departs from prior literature through three key modeling features. First, in our model, an agent's progress towards the goal is not a deterministic function of effort. As is typically the case in real-world settings, progress is positively correlated with effort but the mapping involves a stochastic component. Secondly and quite importantly, it is possible that the innovation in question is not attainable, either because the goal is actually infeasible or because it requires too much effort and resources that it makes little economic sense to pursue. We model such a scenario by having an underlying state of the world (whether the innovation is attainable or not) over which participants have some prior belief. Taken together, these two features imply that an agent's lack of progress may be attributed to either an undesirable underlying state (the innovation is not attainable) or simply to the fact that the agent was unlucky in how her effort was stochastically mapped to progress. Thirdly, we consider a dynamic framework that captures how competition between agents evolves over time and incorporates the fact that agents learn from each other's partial progress to discern the underlying reason for their own lack of progress. In particular, our modeling setup includes well-defined intermediate milestones that constitute partial progress towards the end goal.

We study the simultaneous evolution of the opinion profile and network topology of a system of N agents. Based on the opinion profile at any given time, agents probabilistically decide which other agents to form links with. The probability of a link being formed with another agent depends on both similarity of their opinions and the popularity of that agent. Agents then average their opinion with the opinions of the agents they have formed links with, giving rise to a new opinion profile that determines-in a probabilistic fashion- the network topology for the next time step. Thus both opinions and network structure exhibit a strong correlation over time. Despite this correlation, we show that this system converges to a consensus in opinion. We provide simulations of convergence times and the limiting opinion profile as a function of the parameters of the system.