D&D 5E Swaying a Crowd of NPCs

[Gardens & Goblins]

The more I think about it, the more I think a hard math approach to the problem isn't the right way to handle it. Your tired brain isn't nearly as good an excuse as the fact it's a rather difficult problem! It would greatly reduce the complexity to know whether a PC intends to become a claimant. Maybe that's something you can ask your players between sessions and let us know? (edit: just read this is for a one-shot, so I'm guessing the players don't know this vote is coming?)

Totally agree. The question should be:

What am I trying to achieve here?

If its a political simulation then.. math on.

Else, boil it down to as few die rolls as possible. Focus on giving the party the chance to influence the outcome/utterly balls things up. Then you can focus on arbitrating their clever/depraved antics, throwing Advantage/Disadvantage here and there, calling for skills checks and generally enjoying yourself as a DM.

 

[iserith]

The more I think about it, the more I think a hard math approach to the problem isn't the right way to handle it. Your tired brain isn't nearly as good an excuse as the fact it's a rather difficult problem! It would greatly reduce the complexity to know whether a PC intends to become a claimant. Maybe that's something you can ask your players between sessions and let us know? (edit: just re-read this is for a one-shot, so I'm guessing the players don't know this vote is coming?)

I'm still running some numbers, but I think 77IM has given a decent run down using a minimal number of NPCs to fulfill your stated goals. However, I don't think he's accounting for point 6 above. I'll drop in again later to see what numbers other people are submitting, but if my initial investigation suggests anything, you're looking at closer to 30 or 40 total NPCs to prevent the PC voting bloc from trivializing the encounter, assuming they don't make a claim themselves. If they do, I think you can safely reduce the numbers since it dramatically changes the perspective of undecided voters.

I'm a little busy at work, so I can't respond to everyone's stuff as quickly as I want, but I wanted to touch on this point so that discussion could continue in my short absence from the chat. This is a one-shot (and one that will be replayed many times over with different groups) so I don't know what any given group will choose to do.

My only expectation from a design standpoint is that it should probably be harder for the PCs to take the throne than one of the existing NPC claimants. "Harder" means they have more NPCs to sway than if they were to throw their support behind an existing claimant. I can relent on this point, however, if it simplifies things and/or saves time. Real time is a serious concern because we only have so much time to do a one-shot, so it can't be the case where the players have to convince a ton of NPCs as each interaction takes up time.

Back later. Thanks so much for the discussion and please keep it rolling!

 

[jgsugden]

Simple version:

Set a DC and target time for each NPC. If the PCs spend the target time trying to persuade the NPC, then they get a normal persuasion role against the DC to try to persuade them. If they give a great spiel to you on how they sell the NPC on the PCs, give them advantage. If they spend less than the recommended time or stick their foot in their mouth, give them disadvantage.

At the same time, have the NPCs approaching people and spending time trying to persuade them. Persuading someone that has already decided should be about 5 higher than convincing some that is undecided, but you can fluctuate the DCs based upon circumstance (an NPC dwarf might be better persuaded by a dwarf, etc...)

In the end, when it is time to vote, the PCs should not have had enough time to try to persuade everyone - and there may be people they thought they won over that the NPCs turned (or vis versa). Anyone that is still undecided should flip a coin or - if only partially converted in your mind, might role a die to determine how they vote (not literally).

That is how I'd handle it. As there is not enough time to talk to everyone, all the PCs are encouraged to participate, even if social skills are not usually their forte - perhaps requiring the PCs to figure out who the best targets for the awkward uncharismatic PCs might be...

 

[iserith]

Some thoughts before getting into the maths:

1) Are the NPCs allowed to abstain from the vote? If so, you can use this to tweak the results to your liking and create the appearance of a closer call for the purpose of drama after the dice have already been rolled. On a related note, how is the vote actually performed? Anonymously or openly? Names dropped in a hat? Raising of hands?

The NPCs must declare their loyalty openly at a certain point once the PCs have had a chance to influence events. I don't prefer to modify results based on drama. I like to set the stage in such a way that it can go a number of ways and play to find out what happens. In addition to giving the players the best chance to succeed or fail based on their own merits, it makes the game much more replayable for me as I run different groups through it. (And more replayable for players who want to run through the scenario again with a different group and character and try different things.)

2) If the difficulty in managing a large fight is a concern, NPCs can flee, cower, feint, stand back, or otherwise not participate in the brawl. This is assuming we're not dealing with a warrior culture and everyone has a battle axe on the table.

3) If you allow NPCs to vote in absentia (e.g. they send a sealed letter stating their vote), you can increase the number of NPC votes to whatever number makes the maths ideal for your purposes. Obviously all such votes would belong to the "decided" category. This could be useful if you end up needing or wanting more voters while keeping the number of potential combatants manageable.

It's a Viking-esque culture. That said, I can always upgrade or downgrade the stat blocks to make it suit the difficulty I'm going for. I'm not too concerned with this bit or any related concern.

4) Even if the NPCs can't or won't abstain, can the PCs? I don't know exactly how they won the right to vote in this situation or whether that's even relevant, but I'm curious to know, if you don't mind sharing?

Why they have a say will be established by the players at the start of the game essentially. The NPCs will not abstain. I suppose the PCs could, though it's not clear why they would.

5) I assume the PCs will all vote for the same claimant, whether its one of their own or an NPC. If that's uncertain, it becomes increasingly difficult to set an appropriate number of decided and undecided NPCs.

Yes, we will establish that the PCs' loyalty is to each other first and can thus count on them voting in the same direction.

6) The undecided NPCs can't all be truly, 100% undecided can they? If the PCs didn't intervene, wouldn't they have at least a slight preference? If this is the case, the PCs don't even need to convince the undecided voters who would've sided with them anyway.

For the sake of managing the game and creating a set challenge, the NPCs are either decided or undecided. The NPC claimants can sway the undecided voters or even committed voters if they're desperate. In many cases, they may be directly opposing the PCs in trying to win them over to one side or another.

I imagine that failure to sway an undecided voter in a particular direction results in siding with the opposite camp. Committed voters are harder to sway and failure to sway means they can no longer be moved off their position. This will make resolution quick and decisive I think, plus it will shut down retries at a certain point.

 

[77IM]

[MENTION=6783882]Nevvur[/MENTION]: You're right about the undecided voters. If we assume that each one flips a coin just before the vote, then it's likely that the PCs' candidate can still win even if they haven't secured enough votes. That changes the math a little bit, but not by much, especially if you assume that most players won't stop schmoozing until they know they have enough votes.

I imagine that failure to sway an undecided voter in a particular direction results in siding with the opposite camp. Committed voters are harder to sway and failure to sway means they can no longer be moved off their position. This will make resolution quick and decisive I think, plus it will shut down retries at a certain point.

I love the idea of displaying this as a state machine for each NPC:
Strongly Decided <---> Decided <---> Undecided

If it were me, I would lay out a map of a Viking hall, and arrange the NPCs according to the state machine. Undecideds in the middle, Strongly Decideds in the corners (initially only the candidates themselves) and regular Decideds in between. This provides a really immediate visualization of the current state of the vote and also immediate feedback for how the PCs are swaying things.

 

[iserith]

Okay, based on [MENTION=12377]77IM[/MENTION]'s math and on the assumption that everyone including the claimants get a vote (which I wasn't counting previously), I think this is reasonable:

There are 23 total participants including the claimants, the decided and undecided NPCs, plus the PCs. Claimant A and B each start with 3 decided votes, including themselves. The PCs are a single voting bloc. This means there are 12 undecided voters.

If the PCs throw their weight behind Claimant A or B, they need to get 4 undecided voters to come to the side of the claimant to get the majority. If the PCs make a claim for themselves, they need 7 undecided voters to come to their side.

Does that seem right? Anything I'm not seeing or could stand to tweak?

 

[iserith]

@Nevvur: You're right about the undecided voters. If we assume that each one flips a coin just before the vote, then it's likely that the PCs' candidate can still win even if they haven't secured enough votes. That changes the math a little bit, but not by much, especially if you assume that most players won't stop schmoozing until they know they have enough votes.

I love the idea of displaying this as a state machine for each NPC:
Strongly Decided <---> Decided <---> Undecided

If it were me, I would lay out a map of a Viking hall, and arrange the NPCs according to the state machine. Undecideds in the middle, Strongly Decideds in the corners (initially only the candidates themselves) and regular Decideds in between. This provides a really immediate visualization of the current state of the vote and also immediate feedback for how the PCs are swaying things.

It'll be on Roll20, so I've got a beautiful color high-def map of the Viking hall and there will be a token for each NPC that has a little colored status dot which will correspond to a particular claimant. No status dot means undecided.

 

[77IM]

Does that seem right? Anything I'm not seeing or could stand to tweak?

As Nevvur pointed out, if you assume that the undecideds vote totally at random, or abstain, then the candidate the PCs back is statistically likely to win even if the PCs talk to no one at all. I think that's totally fine -- it makes it an easy victory, but I suspect that the players won't realize it's an easy victory, at least not until they've gotten a bunch of interactions. Plus, if the undecideds vote at random, it could be risky; the only guarantee of victory is to secure enough votes.

One way to get around this is to introduce a contrarian block that is opposed to the PCs and determined to vote AGAINST their candidate out of spite, which evens out the numbers before the PCs get to schmoozing. That seems kind of lame, though, and probably unnecessary unless your players are really good at math and willing to take risks.

Another mechanism is to have no set voting time, and instead say "first candidate to get 12 declarations of support, wins." Thus the undecideds won't ever help determine the majority, but they aren't really abstaining, either; it's like there isn't a quorum. Of course in a one-shot you'll need a time limit of some kind, so maybe if there's no clear winner after a while, they use trial-by-combat or they let the oracles decide or something. In this case, an undecided vote is kind of like voting for that fallback strategy.

I'm probably overthinking this, because if your players are engaged with the scenario, they are going to start hustling at their first opportunity. With 12 undecideds, it's highly unlikely that the PCs will alienate so many of them that it's impossible to get the 4 or 7 votes they need to be certain of victory.

 

[iserith]

Another mechanism is to have no set voting time, and instead say "first candidate to get 12 declarations of support, wins."

That's basically my plan. And it's the PCs doing all the heavy-lifting. It's their game to win or lose since failure to sway an undecided voter puts them in the opposite camp. It'll get decided one way or another and it shouldn't take too long.

Once the decision is made, one or more groups is not going to be happy and that will determine the difficulty of the violence that follows. PCs claiming the throne for themselves will likely have the hardest time in this phase since they'll have shafted the two higher-CR NPCs, plus anyone who sided with them before the PCs achieved a majority. And that feels about right. But, hey, there's a giant-slaying greataxe up for grabs if they prevail which may be quite useful in subsequent scenes.

 

[Nevvur]

An idea for managing the amount of time spent on interacting: there could be smaller voting blocs among the NPCs who share a particular interest. Like maybe there's a group of 3 undecided who need assurances of protection against giants, a group of 4 who are only siding with claimant A because he's bribing them and only need a bigger bribe to switch allegiance, etc. It then becomes a matter of speaking to their representative rather than each member.

You should probably still take into account the likelihood of success for any given interaction when determining specific numbers of determined and undetermined voters, and that's what really complicates the matter when trying to arrive at a 'balanced' social challenge. If we assume a 65% success rate (the baseline "average difficulty" success rate baked into 5e maths), the PCs win 99% of the time. Basically, treating the undecided voters as easy to persuade will trivialize the encounter. This is assuming the PCs don't make a claim themselves, by the way.

The thing I sense most people are missing in this equation is that the PCs don't really need to persuade any undecided voters who are already on their side. There are confounding elements in play, such as the NPC claimants getting to convert them as well, but to provide the most simplistic view of the problem I see, I'm ignoring that for now. The only actors who matter are the undecided voters who disagree with the PCs' choice. Using the figure of 12 undecided voters who are evenly split, the PCs have already won 11:6, and that's before any attempt to persuade them has occurred. Using 65% success rate, it becomes 16:2.

In my estimation, the numbers need to start out stacked against the PCs' candidate. I don't see any other way around it. I would have all (or most) of those undecideds default to voting for a single claimant - the one the PCs haven't chosen. Perhaps he has the strongest claim, even if it's not signficantly stronger than the other claimant's. Unfortunately, I don't have any good ideas for ensuring the PCs wouldn't just switch sides once the stronger claim is made known.

Moreover, the target success rate for converting undecided voters to the PCs' preference needs to be below 50% or the overall odds of success are far too high.

Soooooo, something like this:

5 PC votes for claimant A.
4 NPC votes for claimant A.
4 NPC votes for claimant B.
0 undecided NPC votes defaulting to A.
12 undecided NPC votes defaulting to B.

<10% chance to convert claimant B's hardcore supporters.
30% chance to convert the undecided supporters for claimant B.

This will give the PCs 0-1 hardcore conversions, and 3-4 undecided conversions, for a total of 12-14 votes (5 PCs, 4 determined, 3-5 converted). They require 13 to win. Clever ideas and strong role play can be rewarded with advantage or other bonuses, increasing the likelihood of conversions. Laid out like this, hopefully you can determine for yourself what's the best number of voters. You can easily decrease the NPC votes defaulting to B for that purpose, or increase those defaulting to A if you don't mind extra NPCs in play.

Again, this is all assuming the PCs don't make a claim themselves.

(if my math or assumptions appear wrong to anyone, please point it out. A lot of this is coming off the top of my head)

(edit: went back to recheck and made some adjustments to illustrate my point)