Do you think dogs understand the concept of quantity?

edited November 2011 in Behavior & Training
This is something I've been thinking about a lot, for awhile now, and I'm really torn on it. Do dogs understand the correlation between quantity and result (for lack of a better term)?

Like, do dogs understand more food is better than less food? Or that larger treats mean more tasty goodness? Or that a bigger bone is better than a smaller bone?

Or even the flip - more pain is worse than less pain?

If you set up an experiment where you placed 2 bowls in a room with the same food in them, the only difference is that one bowl had more food in it. Then you let a dog come in and eat the food for 45 seconds before the bowls were taken away. If you did that 5 times for each dog, in a group of say 100 dogs, do you think the result would be that the dogs started going for the bowl with more food more often once they learned that they only had 45 seconds to eat... or would it just be random?

I know in training there is the concept of a "jackpot", where you give a dog more treats for performing an action really well... but I dunno if it's ever been proven that a dog really understand that the "jackpot" is better because there is more of the treat.

Thoughts?

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Comments

  • Huh, that is interesting. I don't know what to think either. Sometimes it seems like Conker knows he doesn't get as much food as Juneau and Sasha, and othertimes it just seems like he's a greedy snob.
    Whenever I give him the choice of one chew or another, he'll just pick his favorite. But if I dump a bunch of them out he has no idea what to do with them and will look at them in confusion then stare at me until I "fix" it. I think I'll see what happens when I lay out a bigger and smaller chew of the same type and see which one he goes for, or a bowl of more meat and less meat and see which he picks.

  • I use the "jackpot" as a reinforcer when training for Flyball, Rally, Agility, etc, and it's my perception that it is more effective than one treat, after spending the past few years doing some pretty demanding training with the dogs. I don't, however, think of it as a quantity issue in that case, but more of a quality of praise issue. When I give the dogs a jackpot, I'm spending 30 seconds or more praising and feeding. I have no doubt that they remember that as more significant than a single treat, and it does shape their future responses. I do think they can perceive differences in amounts if it is obvious enough. A handful of 5 kibbles is the same as a handful of 6 kibbles, but a full bag dumped on the ground vs a stray crumb, is going to get noticed. I do know that I get lack luster performances when I skimp.
  • edited November 2011
    It's not directly related, but the way you framed your question reminds me of a study done by Friederike Range at the University of Vienna in Austria a few years back. Here's the citation for it, but I haven't had a chance to read it carefully myself:

    Range, F., et. al. (2009) Effort and reward: Inequity aversion in domestic dogs? Proceedings of the National Academy of Sciences 106 (1) 340-345.

    The gist of it as reported by mainstream outlets is that dogs trained to perform some simple trick were happy to perform it with or without reward if they had already been trained to do so. But as soon as they saw some other dog was being rewarded for something that they were doing for "free," as it were, the non-rewarded dogs would start to reject "unfair" offers. They don't talk specifically about quantity though -- it's just about either the presence or absence of a food reward, regardless of quality.

    I thought there was another recent (?) study (don't have a citation right now) that showed dogs really can't count that high anyway. So if you laid out ten treats in one bowl as opposed to twelve treats in another, I doubt the dog will notice a difference. On the other hand, if you consistently laid out MORE treats in a specific bowl, and you were consistent with this practice, then I wonder...
  • I remember that report! It showed that dog understand the concept of fairness. Super interesting.
  • To add, I think dogs absolutely understand the difference between 1 and none, and that more is better.
  • I agree with Lindsay about the "jackpot". It is not the amount of treats but the amount of time given. If quantity of treat mattered like that, then you could get away with giving them one big chunk instead of lots of little pieces.

    It would be interesting to see how such an experiment plays out. I think, depending on how the food is laid, they would go after the bigger quantity purely from the fact that it is easier to see. I think I'm going to try it with my dogs and see what happens, lol
  • Hmm. Interesting question.

    From my experience, dogs (at least B&N and the dogs that I have fostered) understand inequality. Whether or not that constitutes an understanding of quantity, I am not sure.

    For example. If I only have 3 treats, and I give one to one dog and two to the other, the other waits for their second treat and appears to get jealous when it does not come.

    However, if I just put out say, a few treats on the floor for each of them, and one's pile has less than the other, I am not sure that they really care about that. They just gobble them up and beg for more. But if more does not come, they go about their business with no apparent jealously. (And please note, that I use the term jealousy VERY loosely.)

    As for the big bone versus the little bone... I do not think that they associate the size difference with quantity. Now, if I broke the big bone into little pieces, versus just one small bone, they definitely associate that with more. In fact, neither of my girls will eat a big bone until I break it into little pieces for them. Whether this is because they are silly or because they want 'more', I am not sure.
  • I agree with what others have said - I think dogs understand the meaning of quantity, but only if it's obvious/exaggerated.

    London certainly understands when another dog is getting MORE attention or food than he is, even if he's had a treat or attention and London certainly understands that Russell gets "more" food/fixings than he does. There is this "jealousy" (in loose definition) that comes with seeing me fix both their meals. He knows he's getting "jipped". I can't really let London see me make the meals or he sits there waiting like "right, that was nice, but where's the stuff -he- got?"

    I'm not sure if that goes with knowing quantity (as Russell gets MORE food and MORE "treats" on top) or being able to judge "fairness", though.
  • I agree with Lindsay about the jackpot and the more about a quality.

    I have been using the jackpot with mat training, and getting the pups to stay on their mat before I release them. If they are able to stay on their mat while I leave the room, go into another room and come back and they are still there, they get their "jackpot". =)

    Kyuubi is still working on this, but Mika is a pro at it now.
  • Very interesting.. im torn as well. I would like to think that dogs would understand that but its hard to say. A couple different test like what you were explaining would be the best.
  • I always just assumed dogs understood quantity in some way due to "jackpotting". I have never really though about it.

    I imagine dog's minds are much similar to young children, in that they always think more equals better. Several small treats would be favored over one large treat.
  • I'm in total agreement with Lindsay about jackpotting. It's the length of time they are feeling good and receiving praise and with Casey on realizing fairness, but not in quantity.

    Trust me, if dogs thought that more food was better than less food, then Mei would have shown me that at some point. She is competitive with, and jealous of, Koda. She has to make sure that she gets equal treats at all times. She even watches me from across the room to make sure I'm not slipping him any goodies. And if I do, she's right there to call me on it and punk him for it.

    I think she's part Shikoku....seriously. She's smart.
  • I also agree with Lindsay about jackpotting. Bea is definitely more motivated when I spend more time with her. As for large and small, I feel that Bea thinks that she is getting more if I feed her more times (since she has a tendency to scarf down her food). She is more eager to please/do tricks if she sees that I have a lot of food in terms of broken pieces in my hand of the treat. However, if she sees only one treat (even if it's large), she does the command but is not really into it, if you know what I mean.

    @curlytails--thanks for posting the paper...it's really interesting!
  • I'm intrigued by this question! I'm not sure. I see them paying attention to "quantity" but am not sure they get it. Examples: I am giving Bel and Oskar treats. Both are sitting. Bel gets her meds in her treat so sometimes it takes me a little longer to get her treat to her. I give one to Oskar, and there's a longer pause, and I give her one, and he seems to think he didn't get one and should get another. If I give him another, then Bel paws me for her other one too. I see that they are very aware of the other dog getting a treat, but they don't seem to have too much of a sense of oh, wait, I just had one. Or maybe they don't care and just want more!

    My family had an elkhound years ago that was probably the smartest dog I've ever had. We used to do this thing with her when we were eating snacks: one chip for me, one for my mom. I'd count them off: one for me, one for you, then one for Tasha (the dog) but sometimes I'd skip Tasha and if I skipped her, she was very aware that she'd been skipped and she'd bark and paw me. It was quite funny.

    I don't think my anecdotes prove anything much one way or the other, but my sense is that dogs do pay attention to quantity and sometimes even size of things (I've seen Toby reject one bone for a bigger one, for example) but I'm not sure they have much finesse to their abilities!
  • edited November 2011
    Very interesting question! I am convinced beyond a doubt that Argos has object permanence (thanks to his persistence), no matter how rudimentary. Object permanence is a somewhat related question, but of course the problem is complicated by the difficulty in separating the knowledge of quantity from the relative value. "I know that bone is bigger, but this smaller one fits in my mouth so much better" or "I know there's more food in that bowl, but I'm not particularly hungry?" (Very scientific personification.) Can relational quantity (that dog just got a treat, where's mine?) be considered a separate "quantity construct" from physical quantity (I saw three treats, and I've had two, so she's still got one more)?
    Just an aside, but infants as young as 5-months can detect violation of physical qantity in occluder paradigms. How much continuity you want to draw from that depends on how much continuity you want to place on the evolutionary continuity of the mammalian brain, I suppose. :P

    Now I'm going to subject poor Arg to a battery of tests. :(

    @curlytails Would the study with dogs not counting too high be more of a visual and/or short-term memory problem than the ability to understand quantity?
  • I dont think that Kaiya associates bigger with being necessarily better although as an only dog currently, there isnt a "competition". Last night she was chewing an "old" bully stick that had gotten pretty short (maybe down to 1") so I let her keep it, but called her into the kitchen to get a new one. She came and took the new 12" one, put it down next to her and went back to chweing the shorter one.

    I do think she understands "quality" though as she will do ANYTHING for her two favorite treats, hotdogs and peanut butter. She will do tricks for those items that she will not do for say a piece of jerkey
  • From my experience, Kohji understands more equals better, I believe this because he will offer the same trick over and over to try to get more of whatever reward is being offered. He will not stop after one trick and one reward. I have never really offered two different sized bones to him, so I’m not sure how he would choose over and over in that scenario. I do not believe he would continually choose the larger bone, I think he would pick whichever he feels is more valuable according to smell or taste maybe…
  • I know in people, whatever pain is the most current is usually considered the “worst pain they’ve ever had” compared to anything they’ve experienced in the past. It’s hard for humans to compare pain in the now and pain in the past, so I wonder if dogs would feel similar.
  • I think some of them count, and furthermore, I think they often keep a rough running tally. :) I agree with Lindsay that when using food as a reward, the praise/attention given with it is often more important to the dog than the food itself is, but, no matter what the actual reward is, the quantity of reward is noticed.

    I definitely think using Jackpots (whether it be food, play or exuberant praise) in training works. A jackpot is, by definition, an unexpected bonus, and when a dog earns one, you can almost see the wheels turning in their heads as they try to figure out how to make it happen again.

    I think you really start noticing how dogs can "count" when you start competing with them, because most sports do not allow food in the ring, and some sports (ie obedience) do not allow any reward (even verbal praise) to be given while the dog is performing. Honestly, it's pretty easy to train a Shiba or an Akita (the two breeds I've worked with) to do agility or obedience because they are smart and as long as there is nothing more interesting going on and they're getting well paid for their efforts, they're more happy to humor you. It's really hard to make the transition from training to competition with these breeds because, when they find themselves in a distracting environment and their handler suddenly expects them to "work" for free, they usually react as you'd expect any sensible creature to! Often the first run or two goes fine because the dog keeps hoping you're just being forgetful, but eventually they all figure out that you have no intention of paying up, and that's when things get embarrassing.

    There is a way around this, and that is to build up the time between rewards - this skill is closely related to maturity, self-restraint, and trust. If you just decrease the frequency between rewards, the dog will quickly loose interest (who could blame him), so in order to make it worth his while, you need to increase the payout. Here's an analogy - a toddler bribed to do something with jelly beans needs to be paid pretty frequently in small denominations (say, one candy every 30 seconds), a teenager mowing the neighbors lawn needs to be paid more frequently at a moderate rate of pay (say, $20 each mowing), but most adults get paid every two weeks (and we expect to be paid what we're owed). If the adult's boss tried to pay him for two weeks worth of work with $20 (or with a jelly bean), the employee would probably loose faith in the employer and be unlikely to work for him in the future - and that's exactly what happens with a lot of green dog/handler teams in performance sports.

    Anyway, when I'm training my dog, he gets rewards (cookies and praise) in small (but varying) quantities frequently (but not regularly) - remember variable reinforcement (VR) is much more powerful than continuous or fixed reinforcement. When my dog does something brilliant and I want to call his attention to it, he gets a jackpot (a bonus). When my dog is trialling he gets lots of cookies and praise before we go into the ring ("cookies in the bank", or a sort of advance deposit) and then lots of cookies and praise after we come out (the pre-agreed upon payment for services rendered). It's actually a nice little positive reinforcement loop as I like rewarding my dog, and he likes being rewarded by me, so we go into the ring happy and confident and usually come out of the ring successful and happy (that's what I dislike most about traditional training - it's setting up a negative reinforcement loop).

    The actually amount of reward (payment rendered) is far more important for low-drive dogs than for high-drive dogs. Just like with people, if the dog doesn't particularly like his job, the amount he's paid matters more to him. For many years I ran a lazy little Shiba girl whom I used to joke counted the obstacles on every course. Of course, I don't think she actually "counted" them but she was very aware of whether a course was shorter or longer than average and she expected and demanded more treats for running the longer courses than for running the short ones. I laughed about it, but I never had a problem with it as it seemed fair to me.

    We've only had one Shiba whom I haven't been able to teach to wait for a reward. He's our 8 year old rescue Boots. We don't know his full history, but he came to us with a lot of trust issues, and having learned that he could get away with anything by being stubborn. His fortitude is Ghandi-like. He's a cool dog, even if he does drive me bonkers sometimes. Anyway, Boots picked up agility very quickly, but can't go more than 3 or 4 obstacles without a reward, no matter what. You can almost see the thought bubble over his head when asked to do so, "No, sorry, I just can't bring myself to do that. I do understand that you just want one more, and that you'll feed me ten times as much if I just do that one jump, but it's the principle of the thing! You owe me, and I don't work on credit. If you don't like it, play with a different dog. I'm making a point here, and I'm not for sale". I haven't quite given up on the idea of eventually working him through it someday, but, for the moment, he's won.

    With my current dog, James, I can probably get ten minutes of competition-quality work from him if I'm able to us verbal praise (but no physical, play, or food rewards, as in agility or rally). I suspect, even in the best of moods, the most I could expect from him with no rewards at all (as in formal obedience heeling, where you are not even allowed to look at them) would be about a minute. That's the amount of "credit" he's willing to extend to me before I need to pay up. It may not sound like much, but that's actually pretty good and we're slowly building it up. He's a fabulous working Shiba.

    The ability of a dog to extend "reward" credit to a handler is very real and very useful, and based on the dog's ability to keep score. Oh yes, I think they can count.
  • I think there are a few interesting points to discuss here. First, I'm convinced that dogs understand magnitude in general. Here's an anecdote. When I'm training Diesel, I use lots of verbal praise during extended exercises so he knows he's doing the right thing and will continue performing. I have to be careful though. If my praise is too lavish, he loses focus and stops performing. I have to temper the magnitude of the praise, or it is counter productive.

    Behavioral psychology tells us about differential rewards, and variable frequency reward schedules. Differential rewards are definitely a "quantity concept." A perfectly executed behavior gets a higher magnitude reward and a not-perfectly executed behavior gets a lower magnitude reward. And variable frequency reward schedules are definitely a "temporal quantity concept". If you increase the frequency of a reward, the dog is getting a higher quantity of reward in a fixed period. For example, if you give once piece of kibble as a reward and do it once very 10 seconds or once every 30 seconds, the dog will definitely prefer the 6 pieces in a minute to 2 pieces in a minute schedule.

    As for the original idea of testing quantity with food bowls, I think you could try that, but there's some issues with that experimental setup that might confound your results. Specifically, the way in which the dog learns about the time constraints and the influence of removing the bowls, their proximity, etc. can all confuse things. In my opinion, a better way to test it would be to pick two behaviors the dog already knows like "stand" and "down". Put them in a sit, and pay 1 piece of kibble for a down and 4 pieces of kibble for a stand. Let the dog offer the behaviors, don't cue them. See which they gravitate to. Then switch the payement scheme. Pay 1 for a stand and 4 for a down. See how long it takes them to switch. I think you'd be surprised what you find.
  • That is an awesome idea, Dave... I think I may have to try that tonight!
  • @nozomifarm

    I laugh when I read your analogy of a baby/teenager/adult being paid for their work, the differences in payout and the frequencies. I need to keep in mind many of the points you raised that a green handler will encounter when training a Nihon-ken in performance sports. I also like the "cookie in the bank" and "credit extended" analogies too.

    As for whether dogs can count, I think they know the differences, but not really the ability to do addition or extraction. One big piece of food reward is good, but from a training perspective, I don't think it is really that useful as once you give the dog his one big piece of food reward, you are pretty much of the picture. The dog will be focusing on the food, busy munching on his reward, rather than staying connected with you. With smaller, continuous rewards, you keep the dogs engaged with you and your verbal praise or petting (if the dog enjoys physical contact with you). A good analogy of one big piece of rewards vs. smaller piece continuous rewards over an extended period of time is fast food dining vs. fine dining. You give a dog a big piece of food and he gobbles it down and he feels full, but is probably a pretty forgetful experience. The slower, steady dining experience with continuous reward is similar to dining at a nice restaurant. You get more pleasure out of the experience and you remember it much better afterwards.
  • @sunyata: Awesome! Let us know how it goes. :-)
  • That's a good analogy Sandra! I also enjoyed reading Nozomifarms training analagies. How true.
  • Thanks for thinking about this question. You guys may have shifted me from thinking they don't understand quantity to thinking they might...

    Tho I am not sure I agree with every example. Like counting, yea I totally agree that dogs count, but I don't know that they add (which is a requirement for understanding quantity I think).

    Also, in the differential reward training, is it that the dog can tell the difference in the quantity of the reward, or is it that the dog can tell one tastes stronger than the other?

    Lisa - that's a neat story about you elk hound, totally ties into the fairness article mentioned above too!
  • edited November 2011
    I'm going to guess that dogs DO understand quantity and here's why: There was an experiment that was done with rats not that long ago that indicated they had metacognition (the ability to know what they did and did not know). The way that this experiment was conducted was the rats were trained to respond to questions about whether a sound was long or short. A control group was forced to answer questions and given no food if they answered wrong but were given food if they answered correctly. The test group was not forced to answer the question. Their reward system was that they would get no food if they got the question wrong, some food for abstaining and a lot of food for answering correctly. The rats that were able to abstain showed a higher percentage of correct answers, indicating metacognition. That, of course, is not the part of this experiment that is of interest here. The reward system is. Basically, this is an experiment that wouldn't have worked if the rats didn't know what 'more' was and since it would seem to indicate that they did, I would say based on that that dogs do as well, given their greater mental capacity.

    Here's a link to the experiment I mentioned: http://www.sciencedaily.com/releases/2007/03/070308121856.htm
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