Gpt4: To solve this problem, we need to ensure that neither the ambassador of Costaguana is left alone with the ambassador of Buranda, nor is the ambassador of Buranda left alone with the ambassador of Atlantis. Here's a step-by-step strategy:
1. *First Trip:* The general takes the ambassador of Buranda across first. This prevents any initial conflict.
2. *Return Trip:* The general returns alone to the bunker, leaving the ambassador of Buranda on the other side.
3. *Second Trip:* The general then takes the ambassador of Atlantis.
4. *Return Trip with Buranda:* The general brings the ambassador of Buranda back to the bunker. This is crucial because leaving the ambassador of Atlantis and the ambassador of Costaguana alone would not cause any conflict.
5. *Third Trip with Costaguana:* The general then takes the ambassador of Costaguana across the tunnel.
6. *Final Return Trip:* The general returns alone to the bunker for the last time.
7. *Final Trip with Buranda:* Finally, the general takes the ambassador of Buranda across.
This sequence ensures that at no point are the ambassador of Costaguana and the ambassador of Buranda left alone together, nor are the ambassador of Buranda and the ambassador of Atlantis. Thus, the relationships between the nations remain unescalated.
Bing Chat runs on GPT-4, however [1]. And Bing gets this wrong in all 3 of its modes (Creative, Balanced, and Precise) as of time of writing.
Given this experiment and similar others presented around here, it stands to reason that GPTs(**1) often identify(**2) the problem as a "wolf, goat, and cabbage" problem and then merely guess which node of the problem is the middle node (inner node of the "danger to" graph), yielding a 1/3 chance of getting it right by pure luck, resulting in diverse reports here.
(**2) That does not always yield an adequate response beyond the mere permutation of nodes, however. I've been getting the following variants for step 1. from Bing in Precise in response to marginally slightly different rewordings of the same:
- The general escorts the ambassador of Costaguana through the tunnel first. This leaves the ambassador of Atlantis and the ambassador of Buranda in the bunker, but they are not alone because the general is still there.
- The general escorts the ambassador of Costaguana through the tunnel first. This leaves the ambassador of Atlantis and the ambassador of Buranda in the bunker, but they are not alone because they have each other.
and so on.
(**1) I also tried Bard and Llama 2 with even more disastrous results full of nonsense of (**2) kind. The earlier posted response of ChatGPT-3.5 is also prime with these as well.
Re
> By the way, as soon as these systems are able to check their reasoning (i don't think it'll be a huge leap) it's enough to solve reasoning problems with probability >0.1% for example. Because you can just have it do rollouts in its head until it's correct [2]
Mistakes of type (**2) don't seem to be fitting the target of the cyclic refinement you are proposing, as far as I can understand it. These errors aren't getting the logic wrong, but completely butcher the basic relationships of actors, like what it means to be alone, or spatial relationships between the actors and their environment.
1. *First Trip:* The general takes the ambassador of Buranda across first. This prevents any initial conflict.
2. *Return Trip:* The general returns alone to the bunker, leaving the ambassador of Buranda on the other side.
3. *Second Trip:* The general then takes the ambassador of Atlantis.
4. *Return Trip with Buranda:* The general brings the ambassador of Buranda back to the bunker. This is crucial because leaving the ambassador of Atlantis and the ambassador of Costaguana alone would not cause any conflict.
5. *Third Trip with Costaguana:* The general then takes the ambassador of Costaguana across the tunnel.
6. *Final Return Trip:* The general returns alone to the bunker for the last time.
7. *Final Trip with Buranda:* Finally, the general takes the ambassador of Buranda across.
This sequence ensures that at no point are the ambassador of Costaguana and the ambassador of Buranda left alone together, nor are the ambassador of Buranda and the ambassador of Atlantis. Thus, the relationships between the nations remain unescalated.