Lave & MarchChapter 7: Diffusion12/3/12Diffusion: spreading out- Can diffuse a fact or belief or an attitude or behavior or opinions- Big target audience - Everett M. Rogers Diffusion of Innovations Spreading information- About health-promoting behaviors (condoms)- About riskso Texting and driving- About dangerous products or recalls- About your political candidate- About your commercial producto Viral marketing, either in person or on internet xMore topics- Blogs linking blogs- Rumors, gossip- Agricultural innovationso Fertilizero Care of land - Early adopters and opinion leadersBasic Assumptions- For diffusion to occur, people must be connected by a communication linko May be symmetrical or asymmetricalo May be present, absent, or probable- For diffusion to occur, the object of diffusion must be transmitted by the party who has it - For diffusion to occur, the transmission must be accepted by the party who doesn’t already have the object of diffusion- At any point in time, every party either has the object of diffusion or does not- Once a party has the object, s/he never loses itSummary- Contact- Transmission- Acceptance- You have it or you do not- You never lose itDivorce- Modeling intergenerational diffusiono How children “catch” divorce from their parents is roughly the ideao This is a bad way to express it because it seems to blame parents for their children’s actionso Book is copyrighted in 1975Divorce- 4 types of couples:o I. Parents of both H & W are divorcedo II. Parents of H divorced, but not those of Wo III. Parents of W divorced, but not those of Ho IV. Parents of neither H nor W divorced If divorce is contagious, rates should be:- I > II & III > IV- To simplify things initially:o Assume all children marry (within their generation)o Assume each type of couple has same number of kids o Assume that males = females = 50%o Assume that marriage pairings are randomo Assume the initial rate of divorce is 20% - So, if the divorce rate is 20% in generation 1, then:o 20% of H come from divorced parents o 20% of W come from divorced parents- So, of the 20% of H with divorced parents, 20% of them will marry W with divorced parents - Generation 2 looks like:o I. All parents divorced, 4% (20% x 20%)o II. H parents divorced 16% (20% x 80%)o III. W parents divorced 16% (80% x 20%)o IV. Neither divorced 64% (80% x 80%) Have to add up to 1- Add in some contagion assumptions (how infectious divorce is):o 100% with both divorced parents divorceo 40% with one divorced parent divorceso 0% with no divorced parents divorces- One of your best friends got married. You won’t know this unless you were told by those who have known. This is based on the second assumption that for diffusion to take place, the object of diffusion must be transmitted by the person who already has it. o YesDivorce- Can continue this sort of analysis to the next generation- After 5 generations, get table (p. 357)- Algebra supplied (p. 358) Steady State Equilibrium- = Same divorce rate from one generation to another- Algebra p. 359 leads to these possibilities:o D rate is zeroo D rate is 100% o A is 50%- Furthermore,o If a < 50%, D rate approaches 0o If a >50%, D rate approaches 100%Epidemiology -Two key questions:o What is the rate of diffusion?o What is the pattern of diffusion?-Mostly just have models of the rate though12/5/12Model of Information Explosion (Birth Model)-Problem is diffusion of info about new boss-Assumptions:o Each hour, every person who has the info tells 3 people whodon’t have ito Everyone who hears it believes it First Results-At first, Carter knows-Hour 1, Carter tells A, B, C (total =4)-Hour 2, each of the 4 tells 3 people (total= 4 +4x3= 16)-Rate is delta n/ delta t, where n is the number of people -N at start + New delta n/delta t = total at endLimits-The analysis so far (birth model) would lead to more people knowing the information than there are people-Various sorts of things limit the diffusion process-For ex, as diffusion continues, it becomes harder to find someone who doesn’t already knowBirth Model with Limits-Taking the growth limit (eg, number of people in the organization) into account-N= growth limit; n=number who have the info at the start of the time period; t= time period; a=diffusion rateo Delta n/delta t= a n (N-n)o This is the term that puts a limit on the whole equation-NB: really only n is changing through the diffusion process Limits-Delta n/delta t= a n (N-n)-Common sense observationso N will be larger than n until they are equalo The a n term will be small at firsto The (N-n) term will be large at firsto Equation is “a times number who know it time the number who don’t” -To guarantee that n + delta n can’t exceed N, a can’t be greater than 1/N -A worked ex, p. 373-The graph, p. 374 called an ogive (ohjive) it looks like a flat S. (number of people who know is vertical, time is horizontal axis)o Growth in number who know accelerates, with the fastest growth where half of them knowo Flattens out at end, when targets are rare -(N-n)o The number of people who have yet to acquire the diffusion object-What happens to (N-n) during the course of the diffusion process?o ShrinksBroadcast Diffusion-Person-to-person contact up to now-But can also broadcast information, eg, through mass media-Let’s work with the ex of a radio station, and assume that the info only comes from the station- ie, no interpersonal relayingThe Radio Station-Assumptions:o Total audience is 100,000 (N) o At a given hour, only 10% tuned in (a)o The 10% are randomly distributedDelta n/delta t= a (N-n) o As you go through broadcast day, number of targets shrink- listenership has object of diffusiono More effectively you diffuse, faster this will happeno Watch results and decide Diffusion for Radio Station-Graph of diffusion, p. 378-Shape is sort of gentle upward curve, bowed a little toward upper left hand corner-Almost linear, but will obviously flatten when it gets close to 100,000 (N) Three Diffusion Models-Graphs, p. 379- study carefully-Birth process. No limits. What affects a?-a is the diffusion coefficient-Exposureo The easier exposure is, the higher a will be-Transmission easeo Easy, simple rumors will have higher a than complex materialso More important things will move faster-Acceptanceo More credible source, a will be higher-Billboards, sponsored ads on FacebookDiffusion and Adoption-Information can diffuse quickly, yet adoption of the innovation may still be