Matthew effects via team semantics (work in progress) Fan Yang Delft University of Technology, The Netherlands ———————————————————— Joint work with S. Frittella 1 , G. Greco 2 , M. Piazzai 2 , 3 and N. Wijnberg 3 1 University of Orléans, France 2 TU Delft 3 Amsterdam Business School 1/15
The Matthew effect (Merton 1968) For whoever has will be given more, and they will have an abundance. Whoever does not have, even what they have will be taken from them. Matthew, 25:29 2/15
The Matthew effect (Merton 1968) For whoever has will be given more, and they will have an abundance. Whoever does not have, even what they have will be taken from them. Matthew, 25:29 2/15
The Matthew effect (Merton 1968) For whoever has will be given more, and they will have an abundance. Whoever does not have, even what they have will be taken from them. Matthew, 25:29 2/15
The Matthew effect (Merton 1968) For whoever has will be given more, and they will have an abundance. Whoever does not have, even what they have will be taken from them. Matthew, 25:29 2/15
The Matthew effect (Merton 1968) For whoever has will be given more, and they will have an abundance. Whoever does not have, even what they have will be taken from them. Matthew, 25:29 “The rich get richer; the poor get poorer.” 2/15
Matthew effects sociology of science: (Merton 1968) business: social network: 3/15
Matthew effects sociology of science: (Merton 1968) reputation citations business: social network: 3/15
Matthew effects sociology of science: (Merton 1968) + reputation citations business: social network: 3/15
Matthew effects sociology of science: (Merton 1968) + reputation citations + business: social network: 3/15
Matthew effects sociology of science: (Merton 1968) + reputation citations + business: reviews sales social network: 3/15
Matthew effects sociology of science: (Merton 1968) + reputation citations + business: + reviews sales social network: 3/15
Matthew effects sociology of science: (Merton 1968) + reputation citations + business: + reviews sales + social network: 3/15
Matthew effects sociology of science: (Merton 1968) + reputation citations + business: + reviews sales + social network: 3/15
Matthew effects sociology of science: (Merton 1968) + reputation citations + business: + reviews sales + social network: 3/15
Matthew effects sociology of science: (Merton 1968) + reputation citations + business: + reviews sales + social network: 3/15
Matthew effects sociology of science: (Merton 1968) + reputation citations + business: + reviews sales + social network: + 3/15
Data sets and regression analysis Sales Reviews Time 0 2 2010 3 5 2011 6 8 2012 8 10 2013 9 14 2014 12 15 2015 4/15
Data sets and regression analysis 12 10 sales at time t 8 Sales Reviews Time 6 0 2 2010 4 3 5 2011 6 8 2012 2 8 10 2013 0 9 14 2014 2 4 6 8 10 12 14 12 15 2015 reviews at time t − ℓ 4/15
Data sets and regression analysis 12 10 sales at time t 8 Sales Reviews Time 6 0 2 2010 4 3 5 2011 6 8 2012 2 8 10 2013 0 9 14 2014 2 4 6 8 10 12 14 12 15 2015 reviews at time t − ℓ s ( t ) = β 0 + β 1 r ( t − ℓ ) + ǫ , where β 1 > 0. 4/15
Dependence relation Dependent variable Independent variables x 1 ... x n w 1 w 2 y t 1 ... 2 3 2000 ⋮ ⋮ 3 ... 5 6 2001 6 ... 7 10 2002 ⋮ ⋮ 7 8 15 2003 ... 12 8 21 2004 ... y ( t ) = β 0 + β 1 ( x 1 ) ( t − ℓ ) + β 2 ( x 2 ) ( t − ℓ ) + ⋅⋅⋅ + β n ( x n ) ( t − ℓ ) + ǫ 5/15
Dependence relation Dependent variable Independent variables Time variable x 1 ... x n w 1 w 2 y t 1 ... 2 3 2000 ⋮ ⋮ 3 ... 5 6 2001 6 ... 7 10 2002 ⋮ ⋮ 7 8 15 2003 ... 12 8 21 2004 ... y ( t ) = β 0 + β 1 ( x 1 ) ( t − ℓ ) + β 2 ( x 2 ) ( t − ℓ ) + ⋅⋅⋅ + β n ( x n ) ( t − ℓ ) + ǫ 5/15
Dependence relation Dependent variable Independent variables Time variable x 1 ... x n w 1 w 2 y t 1 ... 2 3 2000 ⋮ ⋮ 3 ... 5 6 2001 6 ... 7 10 2002 ⋮ ⋮ 7 8 15 2003 ... 12 8 21 2004 ... y ( t ) = β 0 + β 1 ( x 1 ) ( t − ℓ ) + β 2 ( x 2 ) ( t − ℓ ) + ⋅⋅⋅ + β n ( x n ) ( t − ℓ ) + ǫ y ( t − ℓ ) = β 0 + β 1 ( x 1 ) ( t − 2 ℓ ) + β 2 ( x 2 ) ( t − 2 ℓ ) + ⋅⋅⋅ + β n ( x n ) ( t − 2 ℓ ) + ǫ y ( t ) − y ( t − ℓ ) = β 1 (( x 1 ) ( t − ℓ ) − ( x 1 ) ( t − 2 ℓ ) ) + ǫ y t If β 1 > 0: x t − ℓ y t − ℓ x t − 2 ℓ 5/15
Dependence relation Dependent variable Independent variables Time variable x 1 ... x n w 1 w 2 y t 1 ... 2 3 2000 ⋮ ⋮ 3 ... 5 6 2001 6 ... 7 10 2002 ⋮ ⋮ 7 8 15 2003 ... 12 8 21 2004 ... y ( t ) = β 0 + β 1 ( x 1 ) ( t − ℓ ) + β 2 ( x 2 ) ( t − ℓ ) + ⋅⋅⋅ + β n ( x n ) ( t − ℓ ) + ǫ y ( t − ℓ ) = β 0 + β 1 ( x 1 ) ( t − 2 ℓ ) + β 2 ( x 2 ) ( t − 2 ℓ ) + ⋅⋅⋅ + β n ( x n ) ( t − 2 ℓ ) + ǫ y ( t ) − y ( t − ℓ ) = β 1 (( x 1 ) ( t − ℓ ) − ( x 1 ) ( t − 2 ℓ ) ) + ǫ y t If β 1 > 0: x � ℓ y x t − ℓ y t − ℓ x t − 2 ℓ 5/15
Team semantics & (In)dependence logic ⃗ ⃗ u w x y t 1 3 2000 ⋮ ⋮ 3 6 2002 6 10 2004 ⋮ ⋮ 7 15 2006 12 21 2008 Team semantics (Hodges 1997) Dependence logic (Väänänen 2007): FO + =( t , y ) Independence logic (Grädel, Väänänen 2013): FO + x ⊥ y 6/15
Team semantics & (In)dependence logic ⃗ ⃗ u w x y t 1 3 2000 ⋮ ⋮ 3 6 2002 a set of assignments s 6 10 2004 ⋮ ⋮ 7 15 2006 12 21 2008 Team semantics (Hodges 1997) Dependence logic (Väänänen 2007): FO + =( t , y ) Independence logic (Grädel, Väänänen 2013): FO + x ⊥ y 6/15
Team semantics & (In)dependence logic ⃗ ⃗ u w x y t 1 3 2000 ⋮ ⋮ 3 6 2002 a set of assignments s 6 10 2004 ⋮ ⋮ 7 15 2006 M ⊧ s x � ℓ y ? 12 21 2008 Team semantics (Hodges 1997) Dependence logic (Väänänen 2007): FO + =( t , y ) Independence logic (Grädel, Väänänen 2013): FO + x ⊥ y 6/15
Team semantics & (In)dependence logic ⃗ ⃗ u w x y t 1 3 2000 ⋮ ⋮ 3 6 2002 a set of assignments s 6 10 2004 ⋮ ⋮ 7 15 2006 12 21 2008 Team semantics (Hodges 1997) Dependence logic (Väänänen 2007): FO + =( t , y ) Independence logic (Grädel, Väänänen 2013): FO + x ⊥ y 6/15
Team semantics & (In)dependence logic ⃗ ⃗ u w x y t 1 3 2000 a team D : ⋮ ⋮ 3 6 2002 a set of assignments s 6 10 2004 ⋮ ⋮ 7 15 2006 M ⊧ D x � ℓ y 12 21 2008 Team semantics (Hodges 1997) Dependence logic (Väänänen 2007): FO + =( t , y ) Independence logic (Grädel, Väänänen 2013): FO + x ⊥ y 6/15
Team semantics & (In)dependence logic ⃗ ⃗ u w x y t 1 3 2000 a team D : ⋮ ⋮ 3 6 2002 a set of assignments s 6 10 2004 ⋮ ⋮ 7 15 2006 12 21 2008 Team semantics (Hodges 1997) Dependence logic (Väänänen 2007): FO + =( t , y ) Independence logic (Grädel, Väänänen 2013): FO + x ⊥ y Inquisitive logic (Ciardelli, Groenendijk, Roelofsen 2011) [stay tuned, stay for the next two talks...] 6/15
Team semantics & (In)dependence logic ⃗ ⃗ u w x y t 1 3 2000 a team D : ⋮ ⋮ 3 6 2002 a set of assignments s 6 10 2004 ⋮ ⋮ 7 15 2006 12 21 2008 Team semantics (Hodges 1997) Dependence logic (Väänänen 2007): FO + =( t , y ) ∃ f Independence logic (Grädel, Väänänen 2013): FO + x ⊥ y × 6/15
Team semantics & (In)dependence logic ⃗ ⃗ u w x y t 1 3 2000 a team D : ⋮ ⋮ 3 6 2002 a set of assignments s 6 10 2004 ⋮ ⋮ 7 15 2006 12 21 2008 Team semantics (Hodges 1997) Dependence logic (Väänänen 2007): FO + =( t , y ) ∃ f Independence logic (Grädel, Väänänen 2013): FO + x ⊥ y × x � ℓ y y ( t ) = α 0 + β x ( t − ℓ ) + α 1 ( w 1 ) ( t − ℓ ) + ⋅ ⋅ ⋅ + α n ( w n ) ( t − ℓ ) + ǫ Definition. M ⊧ D x � ℓ y iff ∃ p ( x , ⃗ w , y ) as above with β > 0 s.t. M ⊧ D x � p ℓ y , 6/15
Team semantics & (In)dependence logic ⃗ ⃗ u w x y t δ 1 3 2000 2 a team D : ⋮ ⋮ 3 6 2002 2 a set of assignments s 6 10 2004 2 ⋮ ⋮ 7 15 2006 2 12 21 2008 2 Team semantics (Hodges 1997) Dependence logic (Väänänen 2007): FO + =( t , y ) ∃ f Independence logic (Grädel, Väänänen 2013): FO + x ⊥ y × x � ℓ y term ℓ ∶∶= δ ∣ k δ y ( t ) = α 0 + β x ( t − ℓ ) + α 1 ( w 1 ) ( t − ℓ ) + ⋅ ⋅ ⋅ + α n ( w n ) ( t − ℓ ) + ǫ Definition. M ⊧ D x � ℓ y iff ∃ p ( x , ⃗ w , y ) as above with β > 0 s.t. M ⊧ D x � p ℓ y , 6/15
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