## 4 Previous Work
### Paradoxes in Operations Research  
In teaching operations research and artificial intelligence courses, the authors have found that presenting counterintuitive or paradox-like anomalies can be a great eye-opener for listeners. Studying such anomalies leads to a better understanding of algorithms and a deeper learning of operations research and AI techniques. A typical example is the famous Braess paradox that arises in dynamic transportation networks and states that \"_adding a new wide road to a congested transport network can lead to an increase in overall travel time_\" [24,25]. Similar counterintuitive effects are known to also occur, for instance, in power transmission systems [26], biological and ecological systems [27], and exploiting generative artificial intelligence [28].  
A mechanism of this paradox can be explained by changing drivers' priorities and behaviors after a network's reconstruction. For example, in response to a capacity addition, more drivers begin to use the expanded highway; those previously not traveling at peak times shift to the peak hours, and public transport users shift to driving. From a mathematical perspective, such drivers' behaviors disrupt the equilibrium and lead to suboptimal traffic flow for everyone. This is because the Nash equilibrium of such a system is not necessarily optimal. The network change induces a new game structure between multiple drivers, which leads to a new situation. Unlike a Nash equilibrium, where drivers have no incentive to change their routes, when the system is not in a Nash equilibrium, individual drivers can improve their respective travel times by changing the routes they take. It follows that drivers will continue to switch until they reach a new Nash equilibrium, despite the reduction in overall performance.  
Another phenomenon called the Jevons paradox describes a situation where technological progress increases the efficiency of resource use, reducing the amount required per user and lowering its cost. However, the falling cost of use increases demand. Consequently, while individual resource consumption decreases, total societal resource use by all users increases, regardless of whether this resource is fuel, a computer, or an electronic device. Therefore, this \"paradox\" is explained by the substantial societal increase in demand, which outweighs individual gains in resource efficiency, leading to a net increase (rather than decrease) in societal resource consumption [29,30]. These paradoxes warn against making decisions based solely on local or individual optimization without assessing the broader impact on the system.  
One more paradox arising in scheduling theory was described by [PERSON] and [PERSON] [31] and states that \"_increasing the speed of some machines in a no-wait flow-shop problem can significantly worsen the optimal total time_\". There are other, less well-known anomalies studied in literature, for example, the so-called \"_more-for-less paradox_\" in the classical transportation problem [32] and [PERSON]'s multiprocessor scheduling anomaly [33].  
The next sections present another paradoxical \"more-for-less\" phenomenon, according to which increasing generative AI's reliability decreases its efficiency. Note that in all mentioned papers and in this one, the word \"paradox\" is used to denote a counterintuitive and surprising phenomenon, not a classical paradox in the context of formal logic.