Well, I figured that LPIII's been out for a while now, so it might be time to do one of these like I did with the earlier LP packs.
So, the format will be similar. Each rank will be divided into two groups. Group 1 will be levels 1 to 9, and Group 2 will be levels 10 to 17 (or 18, for Dodgy). Following those voteoffs, the winners from each group within a rank will be voted off, and then finally, those winners, with one more round between the top two levels from the first winners round.
So,
Timid 1-9 (2 votes): Timid 3 "Strike It Down!", Timid 4 "Roundabout Run", Timid 8 "Scatterlem"
Timid 10-17 (2 votes): Timid 10 "What Does This Button Do?", Timid 15 "Locked Out!"
Dodgy 1-9 (2 votes): Dodgy 7 "Experimental Materials", Dodgy 8 "Synergistic Effect"
Dodgy 10-18 (2 votes): Dodgy 11 "Extra Skill Required"
Rough 1-9 (2 votes): Rough 7 "Hardwired!"
Rough 10-17 (2 votes): Rough 13 "Shmooth Shailing"
Fierce 1-9 (2 votes): Fierce 1 "Dead Is The New Black"
Fierce 10-17 (2 votes): Fierce 13 "Crossover Arena"
Timid's winners (2 votes): Timid 15 "Locked Out!"
Dodgy's winners (1 vote): Dodgy 8 "Synergistic Effect"
Rough's winners (1 vote): Rough 7 "Hardwired!"
Fierce's winners (1 vote): Fierce 13 "Crossover Arena"
Rank winners (2 votes): Dodgy 8 "Synergistic Effect", Rough 7 "Hardwired!"
Final (1 vote): Rough 7 "Hardwired!"
Bonus round (Winner of voteoffs vs all-time winner from previous voteoffs)
Genius 8 (LPII) "Panic Attack" vs Rough 7 (LPIII) "Hardwired!"
Winner: Genius 8 (LPII) "Panic Attack"
I'll decide on the vote limits for later rounds based on how many levels qualify, rather than attempting to decide them upfront. Most likely it'll be one per round, but if there's especially large ties, it might be two or even three. And then for fun, once we have a winner, I'll do a voteoff between it and the overall winner from previous packs (which was Genius 8 "Panic Attack" from LPII).
EDIT: Okay, so for the playoffs between rank winners, two votes for Timid due to the large amount of qualifying levels, one vote for the other ranks. After that, the winner(s) from each rank will be in a two-vote round, with the top two levels (even if they're not tied) entering a final round with one vote.
As with the last ones, I'll make some predictions. Of course, I haven't received as much feedback, so I'm less confident of these than I was with previous packs.
Timid winner: "Locked Out!"
Dodgy winner: Either "Extra Skill Required" or "The North Korean Method"
Rough winner: "Viva Las Lemmine"
Fierce winner: "Crossover Arena"
Overall winner: "Viva Las Lemmine"
EDIT: Okay, two of those levels were knocked out in the first round, including my overall winner prediction, so here's my new ones based on the first round results:
Timid winner: "Locked Out!"
Dodgy winner: "Extra Skill Required"
Rough winner: "Hardwired!"
Fierce winner: "Crossover Arena"
Overall winner: "Extra Skill Required"
Yay for three-way ties.

We sure seem to get a lot of those in these voteoffs.
In this case, it's between Timid 3 "Strike It Down!", Timid 4 "Roundabout Run" and Timid 8 "Scatterlem". The last one being the only one that I myself voted for.

My other vote was for Timid 6 "The Rebound".
Next round is up!
Two-way this time, between Timid 10 "What Does This Button Do?" and Timid 15 "Locked Out!".
My votes this round were Timid 12 "No Floaters, Guaranteed" and Timid 15 "Locked Out!".
New round is up.
Two-way between Dodgy 7 "Experimental Materials" and Dodgy 8 "Synergistic Effect". I fully expected the latter, not so much the former. My votes were for the latter, and Dodgy 1 "Boost Jumper". Seems very unanimous this time too - apart from my vote for Dodgy 1, there was only one other vote that wasn't for either of the two winners. :O
New round is up!
Okay, well there's our first non-tied round! Dodgy 11 "Extra Skill Required" is the clear winner! (As a point of interest, the remaining votes were split equally between Dodgy 13 "Flag Games" - very unexpected! - and Dodgy 17 "The North Korean Method".)
New round is up.
Alright, so our winner from this round is Rough 7 "Hardwired!". While I did expect that level to do well, I didn't expect it to win - I was expecting Viva Las Lemmine to. o_O (I voted for both of those two myself.)
Anyway, next round is up.
I found this round a bit hard to vote in - I won't say what my votes were until this round's over, but in general, especially after the original Rough 14 was moved to Rough 8, there aren't so many levels that I like that much towards the end of Rough.
Winner from this round is Rough 13 "Shmooth Shailing"! My votes were for it and "Lem Particle".
Next round is up. Now, this has a lot more levels that I really like in it - which also makes it hard to choose. xD
By the way, I noticed one person voted for Rough 17 - does that mean this person's beaten that level? Just wondering because currently, it's still on the list of levels that haven't been beaten by anyone yet. (Indeed, I'd find it quite surprising if it hadn't been beaten; it's not overly hard.)
I think it was me that voted for Rough 17. I still haven't solved it yet, but I believe that it's a great backwards-walking puzzle that'll keep me guessing. I wasn't so sure whether to go for 11, 12 or 17, so as I had to vote for two levels, I went with 12 and 17. I thought you were allowed to vote for levels that you haven't beaten yet (that's why they're in the poll anyway).
Yep, of course you are - I just wondered, because I wanted to remove it from the unbeaten levels list if it *had* been beaten.
Bit of variety in the votes here, and a new record for
how many people have voted! I'm surprised to see Fierce 4 get any votes, let alone two, as that's a bit of a long dragged-out level; there again those kind of levels are very rare in LPIII, so maybe that's why.
My votes went to Fierce 1 and Fierce 8. The former has always been one of my favorites, while the latter is partly due to how impressed I am with how hard people are finding it, and partly because I do find it quite fun - I also like, and this somewhat spoils the solution so I'll spoiler it:
...how, with the correct solution, everything falls almost perfectly into place, rather than needing the kinds of fine-tuning that some timing-dependant levels have.
This round did have another single clear winner; and that was Fierce 1 "Dead Is The New Black".
New round is up.

Before voting, I encourage you to have another go at the two secret levels; they both have pretty clever solutions and haven't been beaten yet (as far as I'm aware).
I left this one going a bit longer because the votes weren't coming in so fast, but I think it's time to move to the next round now. At any rate, it would've taken at least two more voters to simply make it a tie (let alone a different winner) anyway, and we've only had one round so far with that many voters.
So, our winner is Fierce 13 "Crossover Arena". Which was one of my votes too, along with Fierce 11 "The "Lemming" Experiment".
So, we have all our winners from the first set of rounds. Time to start playing the winners off against each other! Note that the number of votes allowed will differ between rounds in some cases here (due to large numbers of winners), so pay careful attention!
Alright, we have a winner! Timid 15 "Locked Out!"

Next round is up.
Oops! I accidentally voted twice when I was clearly asked to vote for one. Anyway, I'm going for Synergistic effect, rather than Extra Skill required, where my other vote was placed.
No worries, I'll keep that in mind when I end this round (probably fairly soon). Unfortuantely, the forum doesn't allow changing the number of votes when editing a poll; I can only change the options themself and reset the vote counts, so that's why it's stuck like that. :/
Okay, so Synergistic Effect is our winner for this round! (My vote was Extra Skill Required.)
New round is up!
Interesting! I've only just voted and in less than three hours I think we have a consensus already, given the small number of users in the forum anyway. I voted for Hardwired, and now it's 4-1 Hardwired last time I looked.
Yep, that's probably one of the closest-to-unanimous rounds in any of the voteoffs so far. So yep, Rough 7 "Hardwired!" is our winner!
Now, this next round will be interesting, since I don't know that many people have been able to solve Fierce 13...
Alright, clear winner here (3 to 1) is Fierce 13 "Crossover Arena".
Semi-final is now up! Remember, you're allowed two votes this time.
So, our qualifiers for the finals are
Dodgy 8 "Synergistic Effect"
Rough 7 "Hardwired!"
Finals are up, may the best level win!

By the way, a thought I had the other day - what do people think about the idea of having voteoffs like this for the *official* games? Or has it been done at some point?
Alright, so our winner is Rough 7 "Hardwired!"
Bonus round is up.
They're both very colourful levels, but my vote went to Panic Attack. The more skills, the more interesting the level, but still, not too easy either. I like the 2-minute time limit as well, which is just right for the hardest difficulty area.
Looks like this is going to be a completely comprehensive victory for one of the levels. 5-0 Panic Attack so far!
Alright, well we definitely have a clear winner here. Genius 8 "Panic Attack" still retains the title of my best level ever!
I'll leave this topic open a bit longer in case anyone wants to add extra comments, as well as for feedback on my earlier question - would you guys like to see a similar voteoff for the official games?
I probably would like it, but maybe arrange the poll differently this time? For example, instead of selecting a list from each difficulty, having all the Level 1s, 2s, etc together to see which is the best of each level? If this works out well we could even make a level pack showing our favourite levels (although on second thought the learning curve would be too steep e.g. Just Dig followed by the Boiler Room.

)
I was going to keep the same format since it's familiar now, but if people think a different format would work better (perhaps even random selections of levels for each round, rather than in order?), I can do that.
Okay, I'm going to close this topic now. I'll probably do the voteoffs for the official games sometime soon - maybe running them in parallel rather than one at a time - once I come up with exactly how I'll do them (since yes, there are some weaknesses in the current format of doing it rank by rank). If you want to suggest anything for it, PM me.
I'll do a LPIII Bonus Pack voteoff at some point in the future, but obviously not this soon after release.