Penultimate	draft Synthese	forthcoming A	Pragmatic	Argument	against	Equal	Weighting Ittay	Nissan-Rozen	&	Levi	Spectre Abstract We	present	a	minimal	pragmatic	restriction	on	the	interpretation	of	the	weights	in	the	"Equal	Weight View"	(and,	more	generally, in	the	"Linear	Pooling"	view)	regarding	peer	disagreement	and	show that	the	view	cannot	respect	it.	Based	on	this	result	we	argue	against	the	view.	The	restriction	is	the following	one:	if	an	agent,	i,	assigns	an	equal	or	higher	weight	to	another	agent,	j,	(i.e.	if	i	takes	j	to be as epistemically competent as him or epistemically superior to him), he	must be	willing – in exchange	for	a	positive	and	certain	payment	–	to	accept	an	offer	to	let	a	completely	rational	and sympathetic j	choose	for	him	whether	to	accept	a	bet	with	positive	expected	utility. If i	assigns	a lower	weight	to	j	than	to	himself,	he	must	not	be	willing	to	pay	any	positive	price	for	letting	j	choose for	him.	Respecting	the	constraint	entails,	we	show,	that	the	impact	of	disagreement	on	one's	degree of	belief	is	not	independent	of	what	the	disagreement	is	discovered	to	be	(i.e.	not	independent	of	j's degree	of	belief). 0.	Introduction How	do	rational	agents	respond	to	disagreement	with	their	peers?	This	seemingly	simple	question	triggers controversy	even	among	those	who	frame	it	in	Bayesian	terms,	a	framework	that	has	proven	instructive	in the	study	of	rationality.	The	correct	response	to	peer	disagreement	is	controversial,	among	other	reasons, because	it	is	entangled	with	several	difficult	questions	and	issues:	What	is	peerhood?	What	kind	of	evidence justifies identifying	an	agent	as	one's	peer?	What is the	proper relation	between	higher	and lower	order rational	credence	(roughly,	how	should	having	equal	confidence	in	the	adequacy	of	one's	own	response	to evidence	and	another	agent's	response	influence	one's	first	order	belief)?	Is	it	okay	to	count	shared	data	as evidence	against	another	agent's	competence	in	responding	to	this	data? This	paper	attempts	to	make	some	headway	on	the	question	of	disagreement	without	engaging	directly	with these	formidable	issues.	Our	main	contribution	takes	the	form	of	a	pragmatic	constraint	on	the	notion	of peerhood:	if	an	agent,	j,	is	your	peer,	then	assuming	that	j	is	sympathetic	–	she	wants	you	to	gain	as	much	as possible	–	you	should	be	willing	– in	exchange	for	a	certain	payoff	–	to let	her	decide	for	you	whether	to accept	a	bet	with	positive	expected	utility. If you	are	not	willing to	accept this	exchange	even for	a sure 2 payoff,	you	do	not	seriously	regard	j	as	your	peer.	We	also	generalize	this	constraint	to	cover	all	cases	of partial	epistemic	deference,	not	only	the	case	of	peerhood. The	constraint	clearly	conflicts	with	views	–"Steadfast"	views1	–	that	allow	you	to	disregard	a	peer's	degree of	belief	in	a	disputed	proposition,	P,	or	to	regard	her	as	less	likely	than	yourself	to	have	the	correct	degree of	belief	in	P	after	discovering	the	disagreement. Yet	the	pressure	here	on	Steadfast	views	is	not	significant	since	proponents	of	such	views	already	admit	that they	only	regard	a	peer	as	being	equally	likely	to	get	things	right	before	her	degree	of	belief	is	revealed,	but not	after.	So,	although	the	constraint	seems	to	shine	an	unfavorable	light	on	Steadfast	views,	it	does	so,	so to	speak,	on	a	bullet	already	bitten. Views	that	are	expected	to	embrace	our	constraint	are	"Conciliatory"	views	that	distinctly	reject	the idea that	you	can	discount	a	peer's	view	by	comparing	it	to	your	own	degree	of	belief	(relative	to	the	available evidence).2	In	particular,	views	that	advise	convergence	(or	near	convergence)	would	accept	our	constraint after	disagreement	is	disclosed.	This	is	because	when	convergence	is	reached	there	is	no	relevant	difference that would justify rejecting a sure gain. A prominent Conciliatory view, the "split the difference" view, requires	peers	to	converge	on	the	average	of	the	difference	in	degree	of	belief	that	they	find	between	them. This is	the	most	natural	and	straightforward interpretation	of (arguably)	the	most	prominent	Conciliatory view,	which	is	known	as	"the	equal	weight"	(or	EW,	for	short)	view.3	The	constraint	we	offer	seems	to	fit	the EW	view	–	particularly	on	its	split	the	difference	interpretation	–	nicely,	not	only	in	its	convergence	result	but also	in	its	rejection	of	the	idea	that	one	can	change	one's	view	about	whether	one's	peer	is	equally	likely	as oneself	to	get	things	right	in	a	particular	case	by	consulting	one's	own	reasoning	from	the	evidence. Surprisingly, the	EW	view	on the	split the	difference interpretation fails to	meet the	constraint	we	offer. Moreover,	our	argument	applies	equally	well	to	EW	views	that	at	least	sometimes	–	but	not	always	–	require that	peers	split	the	difference	and	converge	(or	come	close	to	converging).4 1	See,	e.g.	Christensen	2011	for	a	characterization	of	this	view. 2	Christensen	2011,	p.	1-2	locates	this	as	the	central	issue	dividing	Conciliatory	and	Steadfast	views. 3	We	thank	an	anonymous	referee	for	another	journal	for	helping	us	see	the	nuances	here. 4	The	"splitting	the	difference"	(averaging	over	the	difference	in	degrees	of	belief)	interpretation	of	the	EW	view	is defended	by	Elga	(2007),	at	least	as	understood	by	Christensen	(2007,	p.	199,	n.	15)	and	others	(see	footnote	10),	and by	Christensen	(2011)	(with	some	qualifications)	and	more	recently	by	Cohen	(2013):	"when	peers	discover	they disagree,	each	should	adopt	the	simple	average	of	their	credences,	i.e.	they	should	split	the	difference	between	their credences.	If	I	am	at	.8	and	my	peer	is	at	.2,	then	we	should	each	move	to	.5." Since	our	argument	applies	to	any	splitting	the	difference	case,	it	also	applies	to	the	Conciliatory	view	developed	by Christensen	in	his	more	recent	(2009)	and	(2011)	publications.	Though	Christensen	distances	his	view	from	the splitting	the	difference	interpretation	of	the	EW	view	(2009,	pp.	758-9),	he	advises	peers	to	converge	in	some	cases (and	within	a	limited	range	of	degrees	of	belief).	The	argument	can	apply	even	after	taking	into	consideration	the 3 More	generally,	our	argument	shows	that	any	instance	of	the	"Linear	Pooling"	view	(LP	view)	–	i.e.	any	view according	to	which	after	learning	the	degree	of	belief	of	j,	i's	degree	of	belief	would	be	a	weighted	average of	his	original	degree	of	belief	and j's	degree	of	belief	–	cannot	respect	a	generalization	of	the	constraint stated	above.	The	generalization	is	the	following	one.	If	i	assigns	a	higher	weight	to	j,	(i.e.	if	i	takes	j	to	be epistemically	superior	to	him),	he	must	be	willing	–	in	exchange	for	a	positive	and	certain	payment	–	to	accept an	offer	to	let	a	completely	rational	and	sympathetic	j	choose	for	him	whether	to	accept	a	bet	with	positive expected	utility.	If	i	assigns	a	lower	weight	to	j,	he	must	not	be	willing	to	pay	any	positive	price	for	letting	j choose	for	him. We	argue	that	any	plausible	interpretation	of	the	weights	in	the	LP	view	(of	which	the	EW	view	is	a	special case)	must	respect	this	constraint.	Thus,	since	the	LP	view	violates	this	constraint,	it	must	be	rejected.	The conclusion	we	wish	to	draw	is	that,	in	contrast	with	a	commitment	to	the	LP	view,	the	effect	that	an	advisor's belief	should	have	on	one's	own	belief,	partially	depends	on	what	that	belief	ends	up	being.	In	other	words, the rational impact of an advisor at any level of authority is not uniform. This makes room for the development	of	a	new	Conciliatory	view	that	calls	for	varying	weights	of impact	that	depend	on	advisors' degrees	of	belief.5	Perhaps	such	a	view	has	already	been	proposed,	by	e.g.,	Kelly	(2010);	the	Total	Evidence view.	6 The	remainder	of	this	paper	is	organized	in	the	following	way.	Section	1	discusses	the	relation	between	the EW	view	and	LP,	presents	the	suggested	constraint	in	a	precise	way,	states	the	main	theorem	that	stands	at the	heart	of	our	argument,	and	demonstrates	the	intuition	behind	it	(the	full	proof	is	in	the	appendix).	Section 2	explains	why	advocates	of	LP	views	must	accept	the	constraint	and	discusses	the	relation	between	our argument	and	other	arguments	against	the	LP	view	one	can	find	in	the	literature.	Finally,	section	3	discusses possible	objections	to	our	argument. rather	daunting	list	of	obstacles	in	articulating	a	principle	for	when	averaging	of	this	sort	is	required	(2009,	766,	note 11).	Moreover,	as	we	will	make	clear,	our	argument	does	not	rely	on	exact	averaging,	in	fact,	it	merely	relies	on "Linear	Pooling,"	i.e.	on	a	view	that	attaches	a	fixed	weight	(e.g.	1/3)	to	a	peer's	degree	of	belief	within	a	range.	So	our argument	also	seems	to	apply	to	Christensen's	(2011)	(e.g.	p.	3,	note	3)	view	that	takes	an	even	bleaker	view regarding	the	exact	impact	a	peer's	view	should	have	at	the	present	stage	of	the	discussion	on	rational	disagreement (2011,	p.	17).	His	remarks	there	suggest	that	he	expects	the	impact	of	a	peer's	degree	of	belief	to	be	less	than	splitting the	difference	but	still	significant,	i.e.	suggesting	that	it	is	fixed.	Our	argument,	however,	goes	against	even	these vague	general	expectations.	This	is	because	respecting	our	constraint	will	entail,	at	the	very	least,	different	levels	of impact	to	different	degrees	of	belief	that	a	peer	may	be	discovered	as	having. 5	We	are	not	committed,	however,	to	the	idea	that	the	resulting	view	will	be	Conciliatory	in	Christensen's	sense.	Such a	view	may	very	well	violate	his	independence	constraint.	See	note	2	above. 6	The	Total	Evidence	view	seems	to	be	committed	to	a	rejection	of	the	constraint	we	offer.	Kelly	(2010)	endorses	the split	the	difference	view	in	cases	where	peers	lose	access	to	their	original	evidence	(when	the	evidence	is	purely psychological	in	his	sense-see	note	20	below).	There	seems	to	be,	however,	no	straightforward	way	for	the	Total Evidence	view	to	escape	our	argument	in	such	a	case.	But	perhaps	there	is	an	externalist	type	of	interpretation	of	the view	that	can	do	this	by	marginalizing	the	role	of	access	to	the	evidence.	This	possibility	will	not	be	explored	here. Thanks	here	to	an	anonymous	referee. 4 1.	The	EW	view,	the	LP	view	and	the	Exchanging	Epistemic	Identity	Principle Two	rational	agents i	and j	have	the	same	body	of	evidence	E.	Their	attitudes	regarding	propositions	are represented by their respective credence (or degree of belief) functions; ci(•) and cj(•). 7 The credence function	of	at	least	one	of	these	agents,	let	us	suppose	it	is	agent	i,	is	defined	over	propositions	of	the	form "j	has	degree	of	belief	x	that	P,"	which	we	label	X	(or	X-type	propositions).	We	will	use	"x"	to	refer	to	the value	of	j's	degree	of	belief	that	P	(i.e.	"X"	refers	to	"cj(P)=x").	Before	discovering	the	disagreement,	then, there	are	expectations	associated	with	all	X	propositions	in	a	partition	consisting	of	j's	possible	credences	for P	(according	to	i). We	assume	that	after	i	learns	one	of	the	X	propositions	to	which	ci(•)	assigns	a	positive	credence	value,	i's new	degree	of	belief	in	P,	ci'(P),	is	equal	to	i's	prior	conditional	degree	of	belief	in	P	given	X.	We	assume,	that is,	that	ci'(P)	=	ci(P|X).	By	using	this	assumption,	we	are	following	the	policy,	here	and	below,	of	characterizing LP	views	(and	the	EW	view	in	particular)	within	the	strictures	of	the	standard	Bayesian	framework.	We	discuss possible	objections	to	this	assumption	in	section	3.	However,	it	is	important	to	stress	that	(like	many	others) we	are	not	claiming	that this is	how	rational	agents reason,	but	merely that reasoning	that is	necessarily inconsistent	with	the	Bayesian	framework	pays	a	theoretical	price	that	needs	to	be	counterbalanced	by	a special	argument.8 The	main	question	that	arises	in	the	setting	just	presented	is	whether	it	is	possible	to	identify	any	compelling restrictions on ci(P|X), (i.e. on i's conditional degree of belief in P given that j believes P to degree x). Intuitively-and we take this to be a major merit of the LP view-the value of ci(P|X) depends on i's assessment	of	j's	epistemic	competence.	The	more	competent	(with	regards	to	propositions	such	as	P)	i	takes j	to	be	(in	a	given	context),	the	closer	ci(P|X)	will	be	to	x.	i's	assessment	of	j's	competence	can	be	represented as i's	commitment	to	a	function	that	specifies	for	every	possible	ordered	pair	of	x	and	ci(P)	(i.e.	for	every combination	of	i's	initial	degree	of	belief	in	P	and	j's	degree	of	belief	in	P),	what	impact	j's	degree	of	belief will	have	on	ci(P|X). "Linear	Pooling" is the	name	given in the literature to	one	possible (but	prominent) restriction	on	this	function: 7 Throughout	the	paper	we	will	assume	that	E	is	shared	between	i	and	j.	This	will	allow	us	to	investigate	the	role epistemic	competence	plays	in	cases	of	epistemic	disagreement	in	isolation	from	informational	considerations. 8	See	Steele	(2012)	and	Lasonen-Aarnio	(2013)	for	two	statements	of	the	kind	of	attitude	(with	some	minor differences)	that	we	prescribe	to.	The	demand	that	a	rational	agent's	response	for	discovering	a	disagreement	will	be consistent	with	Bayesian	updating	is	also	discussed	in	Jehle	and	Fitelson	(2009)	and	Shogenji	(2007).	We	return	to	this issue	in	section	3. 5 Linear	Pooling	(LP):	ci(P|X)	=	wx	+	(1-w)ci(P), for	some	0	<	w	<	1. In	words,	i's	conditional	degree	of	belief	in	P	given	j's	degree	of	belief	in	P	is	a	weighted	average	of	the	two agents'	degrees	of	belief.	The	more	competent	i	takes	j	to	be,	the	higher	the	weight	he	assigns	to	j's	degree of	belief	(we	discuss	the	interpretation	of	the	weights	more	thoroughly	below). The	important	point	about	this	formula	is	that	the	weights	chosen	are	independent	of	j's	degree	of	belief that	P.	i	needs	to	commit	himself	to	a	formula	that	specifies	his	conditional	degree	of	belief	in	P	given	that	j believes	P	to	degree	x,	which	holds	for	any	x.	This	is	exactly	the	claim	against	which	we	argue	in	this	paper.9 What	is	the	alternative?	Well,	the	alternative	we	argue	for	in	this	paper	is	to	simply	reject	this	restriction	on the	way	rational	agents	learn	from	others.	We	do	not	argue	here	for	any	alternative	restriction.	However,	it is	obvious	that	a	natural	guideline	for	the	development	of	an	alternative is	the	following	one:	the	weight agent	i	gives	to	agent	j's	opinion	should	decrease	as	the	distance	between	x	(j's	degree	of	belief	in	P)	and ci(P)	(i's	initial	degree	of	belief	in	P)	increases.	We	are	not	going	to	defend	a	worked-out	suggestion,	though. Possibly there is no rational impact algorithm to defend. In this paper	we	only show that any view that incorporates	(restricted)	linear	pooling	–	of	which	the	EW	views	are	instances	–	is	flawed. Now,	one	special	case	of	LP	–	a	case	that	has	attracted	considerable	attention	in	the	literature	–	concerns the	case	in	which	i	takes	j	to	be	his	peer,	i.e.	i	takes	j	to	be	as	epistemically	competent	(with	regards	to	P-type propositions)	as	he	takes	himself	to	be.	In	such	a	case,	it	is	tempting	to	demand	that	the	weight	i	assigns	to himself	will	be	equal	to	the	weight	he	assigns	to	j.	This	is	naturally,	though	not	necessarily,	understood	as	the EW	view	on	its	split	the	difference	interpretation.10	Assigning	equal	weight	to	your	peer	need	not	mean	that you	should	split	the	difference	with	her,	but	it	has	been	taken	to	mean	that,	at	least	within	a	limited	range 9 At	least	within	a	certain	range	of	values	x	might	take.	It	seems	that	Christensen	(2007),	a	prominent	split	the difference	view	advocate	at	the	time	(but	see	footnote	4	above),	agrees	that	when	distance	is	substantial	enough, applying	the	equal	weight	principle	is	not	necessarily	warranted.	Such	is	the	case,	for	instance,	when	a	peer	is presenting	an	obviously	"crazy"	view	about	relatively	simple	matters.	In	more	recent	writing,	Christensen	specifies another	case	where	if	your	own	credence	is	high	and	so	is	your	peer's,	you	should	perhaps	be	more	confident	that	the proposition	in	question	is	true	even	if	your	peer's	degree	of	belief	is	slightly	lower	than	yours	(Christensen	2009,	759). Yet	for	other	cases,	like	the	one	he	specifies	just	before	giving	this	counterexample,	within	a	range	at	least,	he advocates	splitting	the	difference	(Ibid.	758-9). Since	our	argument	works	against	views	that	restrict	the	LP	formula	to	a	range	of	possible	x	values,	Christensen's counterexamples	–	as	far	as	we	can	see	–	do	not	motivate	a	view	that	goes	far	enough	away	from	LP.	We	see	no reason,	however,	why	a	view	such	as	Christensen's	could	not	incorporate	the	idea	that,	even	if	the	discovery	of	a disagreement	should	not	influence	the	degree	to	which	one	takes	an	advisor	to	be	rational,	the	impact	of	this	view should	not	be	constant	(even	within	a	range	of	values). 10 In	addition	to	advocates	of	the	EW	view	mentioned	in	footnote	3	and	6,	Jehle	and	Fitelson	(2009)	and	Kelly	(2010) formulate	the	EW	as	the	split	the	difference	view,	as	do	also	Enoch	(2010,	p.	2)	and	Wilson	(2010)	as	an	interpretation of	Elga's	(2007)	EW	view.	In	contrast,	Lasonen	Aarnio	(2013)	discusses	the	relation	between	the	EW	view	–	that	one assigns	the	same	probability	to	being	correct	as	a	peer	being	correct	–	and	splitting	the	difference.	She	contends	that the	relation	between	the	two	depends	on	transparency	of	the	agent's	second	order	attitudes. 6 of	values,	the	impact	of	the	disagreement	is	at	least	uniform	and	usually	(at	least	close	to)	the	average	of	the difference	between	the	peers	(i.e.	half	in	the	LP	schema	above).	Here	we	will	follow	this	usage	and	focus	as an	example	on	the	case	where	the	weights	do	entail	averaging	(or	splitting	the	difference).	Nothing	in	our argument	will	depend	on	this	choice,	as	we	show	below. The	Equal	Weight	(EW)	view:	When	i	takes	j	to	be	as	epistemically	competent	as	himself	(regarding	the	matter at	hand):	ci(P|"cj(P)	=	x")	= !"($)	'	( ) Although	the	argument	in	this	paper	applies	to	the	LP	view	generally,	since	some	of	the	discussions	in	the literature	target	specifically	the	case	in	which	i	takes	j	to	be	his	epistemic	peer	and	interpret	this	as	averaging, at	some	points	in	our	discussion	it	will	be	convenient	to	concentrate	on	the	EW	view	as	stated	above.	This	is done	solely	for	the	purpose	of	clarity	of	presentation	and	nothing	in	our	argument	is	restricted	to	this	specific case.	On	the	contrary,	as	will	become	clear	there	is	a	sense	in	which	the	argument	is	even	stronger	when	it comes	to	weights	different	from	0.5. We	wrote	earlier,	informally,	that	the	weights	in	the	LP	view	express	something	like	i's	assessment	of	j's	level of	epistemic	competence	with	regard	to	P.	When	i	takes	j	to	be	his	peer,	he	takes	j	to	be	as	competent	as himself	with	regards	to	P-type	propositions.	What,	however,	does	it	mean	to	take	another	agent	to	be	"as epistemically	competent	as	oneself"	with	regard	to	a	certain	class	of	propositions?	In	the	literature	no	clear answer	to	this	question	can	be	found	beyond	vague	demands	such	as	that	if	i	takes	j	to	be	his	peer	he	must take	j	to	be	as	likely	to	"get	things	right"	as	i	takes	himself	to	be. This,	of	course,	does	not	say	much	until	we	know	what	"getting	things	right"	means	in	the	context	that	the EW	view	advocate	is	envisioning.11	One	strength	of	the	argument	we	offer	here	is	that	it	does	not	rely	on	any specific	interpretation	of	the	weights	in	the	LP	view.	Rather,	it	applies	to	any	interpretation	of	the	weights that	respects	a	very	minimal	pragmatic	constraint	which,	we	believe,	any	EW	advocate	should	endorse.	Here it	is: 11	While	the	answer	to	this	question	is	straightforward	in	a	non-Bayesian	framework	("getting	things	right"	with respect	to	a	proposition,	P,	is	to	believe	P	in	case	P	is	true	and	believe	–P	in	cases	it	is	false),	in	a	Bayesian	framework it	is	not.	Lasonen-Aarnio	(2013)	suggests	that	"getting	things	right"	should	be	understood	in	terms	of	identity	between one's	subjective	probability	and	the	"correct"	evidential	(or	"epistemic")	probability.	She	then	shows	that	such	an understanding	leads	to	some	problematic	results	for	the	EW	view.	This	is,	however,	far	from	being	the	only	possible way	to	interpret	the	phrase.	Another	interesting	direction	is	to	understand	"peerhood"	in	terms	of	getting	equal "scores"	in	some	measure	of	accuracy	(see	for	example	Anders	Levinstein	2015),	and	there	are	also	other	possible directions.	One	of	the	advantages	of	the	approach	we	take	here	is	that	we	do	not	have	to	commit	ourselves	to	any single	interpretation	of	peerhood.	Instead	we	use	our	minimal	pragmatic	constraint	that	any	advocate	of	the	EW	view must	accept	(regardless	of	the	way	she	understands	the	term	"peerhood"). 7 Exchanging	Epistemic	Identity	(EEI)12 Suppose	i	faces	the	following	choice:	i	can	either	accept	a	bet,	or	decline	it	or	pass	the	choice	of	whether	to accept	it	or	not	to	j.	Suppose	i	is	certain	that a) j	is	rational	(in	the	decision	theoretic	sense) and b) j	is	completely	sympathetic	to	i	in	the	following	sense:	if	i	lets	j	choose	for	him,	j	maximizes expected	utility	when	the	utility	used	is	i's	utility	function,	but	the	probability	function	used	is	j's credence	function. Then: 1. If	i	assigns	to	j	a	weight,	w,	such	that	w	≥	0.5,	i	should	be	willing	to	pass	the	choice	of whether	to	accept	the	bet	to	j	in	exchange	for	a	certain	positive	payment. 2. If	i	assigns	to	j	a	weight,	w,	such	that	w<	0.5,	i	should	not	be	willing	to	pay	any	certain positive	payment	in	order	to	pass	the	choice	of	whether	to	accept	the	bet	on	to	j. In	the	next	section	we	discuss	the	EEI	more	extensively.	However,	the	intuition	behind	it	is	clear.	Since	by stipulation	i	is	certain	that	j	is	rational	and	uses	i's	utility	function,	the	only	difference	between	i	making	the choice	and	j	making	it	is	the	probability	function	used. Now, it	does	not	make	sense for i to	pay	a	price just so that the	choice	will	be taken	using	a	probability function	that	i	himself	views	as	an	inferior	one,	and	it	does	not	make	sense	for	him	to	decline	a	certain	payoff just	so	that	the	choice	will	be	taken	using	a	probability	function	that	he	himself	views	as	a	superior	one.	In particular, EW view advocates (in peer disagreement situations) are expected to consider this a kind of deciding-myself-fetishism. Thus,	we	believe	any	plausible	interpretation	of	the	weights	in	the	LP	view	must	respect	the	EEI.	However consider	the	following	theorem: 12	We	thank	an	anonymous	referee	for	suggesting	the	name. 8 Theorem	1 For	any	credence	function	of	i	that	assigns	a	non-trivial	probability	value	to	the	possibility	that	j's	degree	of belief	in	P	is	different	from	i's	degree	of	belief	in	P,	and	for	any	non-trivial	weight,	w:	13 a. Even	if	w	>	1/2	(i.e.	even	if	i	takes	himself	to	be	more	epistemically	competent	than	j),	there always	exists	a	bet	such	that	i	will	be	willing	to	pay	a	positive	amount	of	utility	in	exchange for	letting	j	choose	for	him	whether	to	accept	this	bet. b. Even	if	w	≤	1/2	(i.e.	even	if	i	takes	himself	to	be	less	epistemically	competent	than	j),	there always	exists	a	bet	such	that	i	will	be	willing	to	pay	a	positive	amount	of	utility	in	exchange for	avoiding	passing	the	choice	of	whether	to	accept	the	bet	to	j. The	theorem	shows	that	independently	of	i's	credence	distribution	over	the	partition	of	hypothesis	about	j's degree	of	belief	in	P	(with	one	–	uninteresting	–	qualification:	the	case	in	which	i	is	certain	that	j	holds	exactly the	same	degree	of	belief	as	he	does),	and	for	every	non-trivial	weight,	it	is	always	possible	to	construct	a bet such that i will violate the highly intuitive restriction on the interpretation of the weights we have introduced. It	is	interesting	that	when	w	is	trivial	the	result	no	longer	holds.	This	makes	sense:	to	assign	a	weight	of	0	to an	agent	(possibly	to	oneself)	is	to	ignore	that	agent's	opinion	–	and	if	one	ignores	an	agent's	opinion	there can	be	no	dependency	between	that	opinion	and	the	weight	assigned	to	the	agent. Our	argument	is,	then,	the	following	one.	The	theorem	shows	that	the	LP	view	violates	the	EEI.	However,	the EEI	must be respected by any plausible interpretation of the	weights in the LP view.	Hence, there is no plausible	interpretation	of	the	weights	in	the	LP	view	and	thus	the	LP	view	is	false.	In	the	next	two	sections we	better	defend	that	EEI	and	discuss	several	possible	objections,	but	before	doing	so	it	may	be	helpful	to gain	a	better	understanding	of	the	theorem. 13	We	prove	the	theorem	only	for	the	case	in	which	i	assigns	a	positive	probability	to	a	countable	number	of hypothesis	about	j's	degree	of	belief	in	P.	This	is	so	since	it	is	unclear	how	the	LP	view	should	be	defined	in	the	case	of uncountably	many	such	hypothesis	(due	to	the	fact	that	in	such	cases	each	hypothesis	typically	gets	0	probability).	In any	case,	if	the	LP	view	is	correct	it	surely	must	be	correct	also	for	the	countable	case	and	so	proving	the	theorem	only for	this	case	is	enough.	We	discuss	this	a	little	bit	further	in	the	appendix. 9 The proof of the theorem is in the appendix. However, the intuition behind the proof can be easily demonstrated	using	a	simple	example	that	involves	the	case	of	equal	weights.	Consider	the	following	bet.	If P,	i	gets	1	unit	of	utility;	if	–P	i	gets	0	units	of	utility.	i	has	to	decide	between: a. Accepting	the	bet. b. Rejecting	the	bet	and	getting	a	certain	0.2	units	of	utility. c. Passing	the	choice	whether	to	accept	the	bet	to	j. Suppose	further	that	i	takes	j	to	be	his	peer,	that	i	believes	P	to	degree	0.5	and	that	i	assigns	a	positive	and equal	credence	value	of	0.5	to	only	two	hypothesis	about	j's	degree	of	belief	in	P: X	–	"j	believes	P	to	degree	0.9" Y	–	"j	believes	P	to	degree	0.1" Notice	that	so	far	all	is	good:	the	values	specified	together	with	the	peerhood	assumption	and	the	LP formula	are	in	accord	with	the	Theorem	of	Total	Probability: 1. c(P)	=	0.5	=	c(P|X)c(X)	+	c(P|Y)c(Y)	=	(wic(P)	+	0.9wj)c(X)	+	(wic(P)	+	0.1wj)c(Y)	= (0.5×0.5	+	0.5×0.9)0.5	+	(0.5×0.5	+	0.1×0.5)0.5	=	0.5 Notice	now	that	i's	expected	utility	for	a	(accepting	the	bet)	is	0.5	and	his	expected	utility	for	b	(rejecting the	bet)	is	0.2.	What	is	i's	expected	utility	for	c	(passing	the	choice	to	j)? Well,	if	Y	is	true	(if	j's	degree	of	belief	in	P	is	0.1)	j	will	choose	to	reject	the	bet.	In	this	case,	i	gets	0.2	units of	utility.	If	X	is	true	(if	j's	degree	of	belief	in	P	is	0.9)	j	will	choose	to	accept	the	bet.	In	this	case	i	will	face	a bet	with	expected	utility	of 2. c(P|X)	×	1	+	c(-P|X)	×	0	=	c(P|X)	=	c(P)	×	0.5	+	x	×	0.5	=	0.5	×	0.5	+	0.9	×	0.5	=	0.7. Thus,	i's	expected	utility	from	c	is 3. EU(c)	=	0.5	×	0.2	+	0.5	×	0.7	=	0.45	<	0.5 In	other	words,	i's	expected	utility	from	c	is	lower	than	i's	expected	utility	from	a	and	so	i	will	violate	the EEI:	he	will	be	willing	to	pay	a	positive	amount	in	order	to	avoid	passing	the	choice	of	whether	to	accept	the bet	to	j	even	though	i	takes	j	to	be	as	epistemically	competent	as	himself. 10 In	this	example,	like	in	the	general	proof,	we	take	advantage	of	the	fact	that	if	i	would	pass	the	choice	of whether	to	accept	the	bet	to	j,	j's	choice	would	reveal	to	i	her	degrees	of	belief	in	P	and	thus	when calculating	the	expected	utility	of	passing	the	choice	to	j,	i	must	take	this	under	consideration	(i	must,	that is,	use	his	conditional	degrees	of	belief	given	j's	possible	choices). Thus,	on	the	pragmatic	level,	i.e.	when	it	comes	to	calculating	expected	utility,	the	way	i	treats	j's	opinion does	depend	on	what	this	opinion	turns	out	to	be	(because	j's	beliefs	are	related	to	her	choices	in	a systematic	way)	and	this	pragmatic	dependency	is	translated	using	the	EEI	to	an	epistemic	dependency. 2.	The	EEI	and	other	arguments	against	the	LP	view In	the	literature	one	can	find	several	other	arguments	against	the	LP	view	(and	several	arguments	against the	EW	view	on	its	averaging	interpretation).	A	popular	–	and	quite	successful	–	Bayesian	line	of	argument against	the	LP	view	is	based	on	the	observation	that	it	runs	into	trouble	when	moving	from	the	simple	case that	involves	a	single	updating	after	learning	the	degree	of	belief	of	a	single	agent	in	a	single	proposition	to the	more	general	case	that	involves	successive	updating	on	different	types	of	evidence	that	include	several other	people's	degrees	of	belief	in	several	different	propositions	together	with	some	first	order	evidence. For	example,	Shogenji (2007)	shows	that	there	are	cases in	which	a	Bayesian	agent	cannot	update	(using classical	Bayesian	updating)	his	beliefs	after	learning	both	some	first	order	propositions	and	the	degrees	of belief	of	another	agent	in	some	propositions	in	a	way	that	obeys	the	LP	constraint	without	violating	the	laws of	probability.14	Bradley	(2007)	shows	that	even	when	it	comes	to	a	single	updating instance,	the	LP	view leads	to	problematic	consequences	when	more	than	one	epistemic	peer	is	involved.	For	example,	he	shows that	in	some	cases	a	Bayesian	agent	can	respect	the	LP	constraint	with	regard	to	a	proposition,	P,	only	if	he treats	the	degree	of	belief	in	P	of	one	of	the	agents	to	which	he	assigns	a	positive	weight	as	independent	of the	truth	of	P. Although	we	are	sympathetic	to	these	arguments,	we	do	not	take	them	to	refute	the	LP	view.	First,	there	are some	potential	replies.	For	example,	Jehle	and	Fitelson	(2009)	show	that	there	are	several	variations	of	the EW	view (they	only	deal	with the	split the	difference	EW	view,	not	with the	LP	view in	general) that	are invulnerable	to	the	problem	discussed	by	Shogenji	(2007)	and	Wilson	(2010).	Similarly,	Steel	(2012)	shows that	there	is	an	interesting	class	of	cases	in	which	the	problem	to	which	Bradley	(2007)	points	does	not	arise. 14 Wilson	(2010)	discusses	the	same	mathematical	phenomenon	from	a	different	philosophical	angle. 11 Second,	and	more	generally,	the	existing	arguments	against	the	LP	view:	(1)	Do	not	hold	in	the	case	of	a	single updating	on	the	degree	of	belief	of	a	single	agent	in	a	single	proposition;	(2)	Only	show	that	there	are	cases in	which	the	LP	view	runs	into	trouble.	They	do	not	show	that	the	LP	view	always	runs	into	trouble.	Thus, these	arguments	allow	for	an	acceptance	of	the	LP	view	in	a	restricted	class	of	cases. As	a	matter	of	fact,	there	is	an	extensive	body	of	literature	(that	started	growing	in	the	beginning	of	the	80s) that	discusses the	problem	of	probabilistic	opinion	pooling	using	an	axiomatic approach.15	This literature identifies	several	different	sets	of	axioms	that	uniquely	pick	out	different	methods	of	pooling.	The	LP	method, for	example,	is	the	only	pooling	method	that	respects	the	following	two	axioms:	(1)	Unanimity	Preservation: if	all	the	agents	to	which	i	assigns	a	positive	weight	have	the	same	degree	of	belief in	P	as i, i	should	not change	her	degree	of	belief in	P	after learning	the	other	agents'	degrees	of	beliefs; (2) Independence: i's degree	of	belief	in	P,	after	learning	the	other	agents'	degrees	of	belief,	depends	only	on	the	other	agents' degrees	of	belief	in	P	(not	on	their	degrees	of	belief	in	other	propositions).16 Now,	since	these	sets	of	axioms	are	inconsistent	with	each	other,	and	since	each	one	of	the	sets	seems	to	be the	appropriate	one	to	adopt	in	different	contexts,	it	seems	clear	that	no	single	pooling	method	should	be pointed	to	as	the	right	method	to	adopt	in	every	context.	Rather,	it	seems	that	different	methods	should	be used	in	different	contexts.17	Arguments	such	as	those	of	Shogenji	(2007),	Wilson	(2010)	and	Bradley	(2007) should	be	understood,	we	believe,	as	pointing	to	specific	contexts	in	which	we	should	not	expect	Unanimity preservation	and	Independence	to	hold.	However,	these	arguments	do	not	show	that	the	LP	approach	should never	be	used. Our	argument,	on	the	other	hand,	does	exactly	that.	Our	argument:	(1)	Works	in	the	case	of	a	single	updating on	the	degree	of	belief	of	a	single	agent	in	a	single	proposition;	(2)	Can	be	made	against	any	such	instance	of LP	that	involves	non-trivial	weights	(i.e.	weights	that	are	different	from	either	1	or	0). Our argument can do this because, unlike the arguments mentioned above, it does not point to any problematic	epistemic	features	of	the	LP	view.	Rather	it	rests	on	the	very	weak	pragmatic	restriction	on	the interpretation	of	the	weights	in	the	LP	view	we	have	introduced.	The	power	of	our	argument	depends,	then, entirely	on	the	plausibility	of	the	EEI	from	the	point	of	view	of	advocates	of	the	LP	view. As explained in section 1 the	main idea behind the EEI is that, on the assumption that j is rational and sympathetic	to i (which	we	stipulate is	believed	to	degree	1	by i),	the	only	difference	between	j	choosing 15 See	List	and	Dietrich	2014	for	a	good	introduction. 16 This	was	proven	first	by	Lehrer	and	Wagner	(1981). 17 Thus,	after	discussing	several	sets	of	axioms,	List	and	Dietrich	argue	that	"it	should	be	clear	that	there	is	no	onesize-fits-all	approach	to	probabilistic	opinion	pooling"	(List	and	Dietrich	2014,	p.	20). 12 whether	to	accept	the	bet	and	i	choosing	is	which	credence	function	is	used	in	the	expected	utility	calculation, i's	or	j's.	If	the	weights	express	i's	estimation	of	the	relative	level	of	epistemic	competence	of	himself	vs.	j (with	respect	to	P),	then	violation	of	the	EEI	amounts	to	being	willing	to	pay	in	order	to	make	a	choice	using a	credence	function	that	i	himself	judges	to	be	inferior. From	this	perspective,	the	EEI	can	be	seen	as	a	natural	extension	of	similar	restrictions	regarding	the conceptual	inter-dependence	between	desires,	beliefs	and	actions.	Arguably,	it	is	conceptually	impossible for	a	rational	agent	to	prefer	"x	units	of	utility	if	A	and	0	if	–A"	to	"x	units	of	utility	if	–A	and	0	if	A"	while believing	A	to	a	lower	degree	than	–A.	In	the	same	way	–	if	"epistemic	competence"	is	a	meaningful	term	it seems	to	be	conceptually	impossible	for	a	rational	agent	to	(strictly)	prefer	using	one	probability	function, c(•)	to	using	another	probability	function	c'(•)	in	expected	utility	calculations	while	taking	c'(•)	to	be	more epistemically	competent	than	c(•). When	it	comes	to	the	case	of	peerhood,	this	consideration	is	conceptually	related	to	the	idea	of	symmetry. One	thing	the	EW	view	on	the	averaging	interpretation	(in	particular)	has	going	for	it,	is	that	it	is	symmetric: if	i	and	j	are	peers	(and	know	this)	they	should	treat	each	other	in	the	exact	same	way.	This	symmetry	is	–	at least	according	to	advocates	of	the	EW	view	–	dictated	by	the	concept	of	peerhood.	When	two	rational	agents are	peers,	identity	does	not	matter:	if	a	given	reaction	to	the	disagreement	is	rational	for	one	of	them,	it	is also	rational	for	the	other.	In	the	case	of	the	choice	presented	to	the	agent	in	our	EEI	condition,	if	it	is	rational for	i	to	accept	(or	to	decline)	the	offer	to	let	j	choose	for	him	whether	to	accept	a	bet	(knowing	that	j	adopts i's	utility	function	when	making	the	decision),	it	is	also	rational	for	j	to	accept	(decline)	the	offer	to	let	i	choose for	her	whether	to	accept	the	bet	(knowing	that	i	adopts	j's	utility	function	when	making	the	decision).	Thus, in the case in	which i and j have the same	utility function, there is no	difference	whatsoever between j choosing	and	i	choosing	and	so	a	violation	of	the	EEI	in	the	case	of	equal	weights	amounts	to	a	refusal	to	get a	free	payoff	(which	is	clearly	conceptually	impossible	when	the	payoff	is	in	terms	of	utility).	This	is	so,	it	is important	to	stress	again,	in	the	EW	view's	advocate	own	light.18 Another	reason	the	EW	view	(specifically)	justifies	EEI	is	that	assuming	it	provides	the	rational	response	to disagreement	and	that	i	knows	j	is	rational,	after	credences	are	exposed,	i	will	surely	respect	the	EEI.	This	is because	on	the	EW	view,	if	i	and	j	are	rational,	they	will	converge	-	they	will	have	the	same	credence	for	P and	hence,	whatever	payoff	EEI	offers	will	be	gained	for	free.	In	rejecting	the	EEI	the	EW	view	advocate	would have	to	explain	why	before	discovering	the	disagreement	j's	credences	are	not	to	be	trusted	as	much	as	i's, 18	Thanks	to	an	anonymous	referee	for	the	suggestion	to	justify	the	EEI	by	symmetry	considerations.	This	referee	also suggested	that	there	are	interesting	connections	between	the	EEI	and	some	discussions	in	the	literature,	e.g.,	how Keren	(2007)	understands	deference	in	the	context	of	testimonial	knowledge	transfer.	Unfortunately,	discussing possible	connections	would	take	us	too	far	afield. 13 while	after	the	discovery	they	are	good	enough	to	be	an	equal	basis	for	the	convergence.	It	is	hard	to	see how	this	feat	can	be	accomplished.19	The	argument	we	have	employed	here	is	novel	in	this	sense.	It	focuses on the epistemic constraints imposed by conditionalization and the LP view as employed before disagreement is	discovered.	This	feature	of	our	argument	blocks	any	attempt	to	evade	it	by	pointing	to	a particular	property	of	the	disagreement	itself. In	contrast	to	advocates	of	the	LP	view,	rejecting	the	EEI	does	seem	to	be	a	plausible	option	for	those	who reject	linear	pooling:	if	the	weight	one	gives	to	one's	peer	is	a	function	of	that	peer's	credence	value,	then	it makes	sense	that	one	will	be	willing	to	pass	the	choice	of	whether	to	accept	a	bet	with	a	positive	expected utility	to	one's	peer	only	conditional	on	that	peer	holding	certain	credence	values.	In	other	words,	rejection of linear	pooling	opens the	door to	a	view	according to	which it is	not	possible to	decide	with	complete certainty	whether	someone	is	a	peer	(in	the	sense	of	giving	her	credence	a	certain	weight)	regarding	P	before learning	what	this	person's	degree	of	belief	in	P	is. Proponents of linear pooling cannot, however,	make this	move because they believe that once one has decided	to	treat	another	person	as	one's	peer	with	respect	to	P,	that	person's	degree	of	belief	in	P	will	have the	same	impact	no	matter	what	it	turns	out	to	be	(at	least	within	a	range	of	values).	This	is	the	essence	of the LP view: its commitment to the independence	of the	weight assigned to an agent from that agent's degree	of	belief. Some	scholars	understand,	however,	the	requirement	of	the	independence	of	the	weights	in	a	way	that	is slightly	different	from	the	one	presented	here.	Instead	of	taking	the	debate	to	be	about	whether	the	weight that	i	gives	j's	opinion	depends	on	j's	degree	of	belief	that	P,	they	take	it	to	be	about	whether	the	weight	that i	gives	to	j's	opinion	depends	on	the	reasoning	j	employs	when	adopting	her	degree	of	belief	in	P	(see	for example	Christiansen	2009	and	Elga	2007).20 We	do	not	suggest	that	these	two	formulations	of	the	debate	are	equivalent.	They	are	not.	However,	in	cases (like	those	we	consider	here)	in	which	i	and	j	share	the	same	evidence,	an	important	part	of	what	we	call	"j's 19	One	way,	though,	was	hinted	at	by	a	referee	of	this	journal.	Suppose	we	employ	Kelly's	(2010)	distinction	between the	discovery	of	one's	peer's	reaction	to	the	evidence-psychological	evidence-and	non-psychological	evidence-the original	evidence.	The	EW	advocate	can	claim	that	without	the	psychological	evidence,	a	peer's	credence	is	not	to	be relied	on. We	don't	find	this	line	particularly	plausible,	but	we	don't	want	to	claim	that	no	development	in	this	direction	will work.	Kelly	himself	uses	the	distinction	to	argue	against	the	EW	view.	Roughly,	his	claim	is	that	it	is	implausible	that psychological	evidence	swamps	non-psychological	evidence.	See	note	6	above	for	the	claim	that	Kelly's	Total	Evidence view	is	susceptible	to	our	argument	for	some	cases,	cases	for	which	the	possible	reply	on	behalf	of	the	EW	view	will	be equally	problematic. 20	Here	is	Christensen's	(2011)	formulation:	"In	evaluating	the	epistemic	credentials	of	another's	expressed	belief about	P,	in	order	to	determine	how	(or	whether)	to	modify	my	own	belief	about	P,	I	should	do	so	in	a	way	that	doesn't rely	on	the	reasoning	behind	my	initial	belief	about	P." 14 reasoning"	is	the	impact	the	evidence	has	on	j's	degree	of	belief	that	P.	Although	there	might	be	some	mental activities that should be qualified as "reasoning" and cannot be captured nicely in our setting as either instances	of	identifying	the	evidence	or	as	instances	of	deciding	what	the	impact	of	the	evidence	on	one's degree	of	belief	should	be,	we	ignore	this	option.	By	doing	so	we	only	set	the	bar	higher	for	ourselves:	we show	that	even	when	the	only	difference	between	j's	and	i's	reasoning	is	what	they	take	to	be	the	impact	of the evidence (that they share) on their degree of belief that P, the weight i assigns to j should not be independent	of	j's	reasoning. Thus,	we	conclude	any	advocate	of the	LP	view	should	be	committed to the	EEI	and thus subject to	our argument. 3.	Possible	objections We	have	shown	that	the	LP	view	is	inconsistent	with	the	EEI.	In	the	previous	section	we	have	argued	that	any advocate	of	the	LP	view	must	be	committed,	however,	to	the	EEI.	Thus,	the	conclusion	must	be	that	the	LP view	is	false.	How	else	can	a	LP	view	advocate	respond? One	possible	response	is	to	reject	our	setting	by	arguing	that	it,	in	some	way,	misrepresents	the	LP	view.	We are	not	going	to	respond	here	to	the	general	charge	that	the	Bayesian	framework	cannot	capture	examples of	peer	disagreement	according	to	the	LP	view.	We	take	that	to	be	a	significant	theoretical	cost	in	and	of itself.	The	LP	view	is	not	(and	we	think	it	should	not	be)	viewed	as	opposed	to	Bayesianism.	But	there	are more specific claims that can	be	used to resist conditionalization	within the	Bayesian framework in	peer disagreement	situations. A	seemingly	attractive	way	to	resist	the	argument	above	is	to	claim	that	in	our	example,	at	least,	i	is	certain in	advance	that	j	has	a	different	credence	than	he	has	(though	he	knows	not	which	and	cannot	change	his credence).	Thus	he	knows	that	j	disagrees	with	him.	The	EW	view	(on	any	of	its	interpretations)	concerns	the reaction	to	the	discovery	that	a	peer	disagrees,	so	perhaps	we	are	misrepresenting	the	debate. Attractive	as	this	response	may	seem,	it	won't	do.	It	concerns	our	simplified	example.	It	makes	no	difference to	the	argument,	if	we	add	a	third	X-type	proposition,	say	Z	(where	Z="j's	degree	of	belief	is	0.5"),	such	that ci(Z)=0.8 (and	adjusting i's	degree	of	belief in	X	and	Y	accordingly symmetrically since	X, Y, and	Z form	a partition).	The	theorem	shows	that	the	resulting	case(s)	where	certainty	of	disagreement	is	absent	(and	in fact	i	is	almost	certain	that	there	is	no	disagreement)	will	violate	the	EEI	in	the	same	way	the	example	does. 15 In	general	it	is	interesting	to	note,	though,	that	in	contrast	with	the	cases	presented	in	the	literature,	cases such	as	the	one	in	our	example	show	that	the	discovery	of	disagreement	itself	is	not	an	essential	element	of the	problem	of	peer	disagreement.	What	does	seem	essential	is	the	discovery	of	what	the	disagreement	is, what	j's	degree	of	belief	actually	is,	not	merely	that	j's	degree	of	belief	is	different	from	i's.	If	there	is	a	rational response to the	discovery	of	peer	disagreement, it seems	possible to	construct	cases	where the	possible values	are	balanced in such	a	way that	an	agent	will know that she	disagrees	with	her	peer	but	will	not thereby	be	required	to	change	her	credence	before	discovering	what	the	disagreement	is. Related to the	previous	objection is the claim that the credence function c(•) should	not contain	X-type propositions at all (i.e. hypothesis about j's degree of belief in P). The motivation for this is that the assumption	that	agents	always	start	from	a	prior	probability	distribution	that	is	defined	over	an	algebra	that contains	all	Xs is	so	demanding	that it	makes	any	conclusion	that is	based	on	it	practically insignificant.	A Bayesian	alternative	is	to	argue	that,	upon	learning	agent	j's	degree	of	belief	in	P, i	updates	his	degree	of belief	in	P	in	a	way	that	gives	the	required	LP	view	value,	and	then	after	this	initial	change	he	updates	his degrees of belief in other propositions using Jeffrey conditionalization. The problem to be investigated according	to	this	line	of	thought	is	how	the	initial	updating	should	go.	Thus	the	question	of	peer	disagreement is	not	as	we	have	posed	it,	but	rather:	how	should	agent	i	update	his	degree	of	belief	in	P	after	learning	X having	no	prior	probability	distribution	that	is	defined	over	an	algebra	that	contains	X	to	refer	to? While	it	seems	to	us	that	this	alternative	line	of	representing	disagreements	is	more	focused	on	disagreement and	more realistic,	we also believe that using our previous presentation of the LP view (i.e. in terms of conditional	credences)	carries	no	significant	theoretical	cost.	What	motivates	moving	from	our	way	to	the alternative	is	the	understanding	that	actual	agents	have	limited	cognitive	resources	and	thus	cannot	always anticipate	their	belief	updates	for	learning	each	one	of	the	propositions	that	it	is	possible	for	them	to	learn (and	specifically	propositions	such	as	X).	This	is	one	motivation	for	considering	pooling	strategies	in	general (as opposed to discussing what the conditional credences should be). Thus, when real people learn propositions	such	as	X	they	usually	do	not	have	a	prior	conditional	probability	for	P	given	X	to	refer	to.	We should still demand, however, that any good answer to the question regarding real agents and their limitations	be	consistent	with	the	right	answer	to	the	question	of	disagreement	as	we	have	framed	it.	Agents could,	after	all,	sometimes	at	least,	have	the	required	conditional	degrees	of	belief. We	should	demand,	that	is,	that	the	rational	way	i	updates	his	beliefs	after	learning	X	in	case	c(•)	is	defined over	an	algebra	that	does	not	contain	X	will	be	consistent	with	the	way	i	would	update	his	degree	of	belief	in P	in	a	case	where	c(•)	is	defined	over	an	algebra	that	does. 16 Our	response	to	this	attempt	to	avoid	the	argument	is	also	how	we	would	want	to	answer	worries	in	the same	general	vicinity.	In	general,	we	can	get	to	the	LP	view	values	as	a	response	to	peer	disagreement	either by a non-conditionalization rule or by an anti-conditionalization rule. We have no problem with nonconditionalization	rules	as	such,	but	we	think	they	do	not	avoid	the	argument.	After	adopting	such	a	rule	one would still need to show how the argument is avoided with regard to cases that overlap with conditionalization.	We	do	have	a	problem,	however,	with	anti-conditionalization	rules.	In	fact,	as	much	as we	like	our	EEI	constraint,	we	think	adopting	an	anti-conditionalization	rule	is	a	higher	theoretical	price	to pay	than	rejecting it	simply	because	it	doesn't	accord	with	the	LP	view.	That is,	simply	biting	the	bullet is better	here. To conclude,	what seems	clear is that linear	pooling	– the independence	of the	weight from the	agent's degree	of	belief	–	has	unacceptable	consequences	precisely	because	of	this	independence.	Unless	you	assign a	weight	of	1	or	0	to	the	opinion	of	another	agent,	learning	what	this	other	agent's	opinion	is	must	effect	– contra the EW view – the weight you assign to her opinion. What exactly should this effect be? This, unfortunately,	is	still	an	open	question. Appendix Theorem	1 For	any	credence	function	of	i	that	assigns	a	non-trivial	probability	value	to	the	possibility	that	j's	degree	of belief	in	P	is	different	from	i's	degree	of	belief	in	P,	and	for	any	non-trivial	weight,	w: 1. Even	if	w	>	1/2	(i.e.	even	if	i	takes	himself	to	be	more	epistemically	competent	than	j),	there always	exists	a	bet	such	that	i	will	be	willing	to	pay	a	positive	amount	of	utility	in	exchange for	letting	(a	completely	rational	and	sympathetic)	j	choose	for	him	whether	to	accept	this bet. 2. Even	if	w	≤	1/2	(i.e.	even	if	i	takes	himself	to	be	less	epistemically	competent	than	j),	there always	exists	a	bet	such	that	i	will	be	willing	to	pay	a	positive	amount	of	utility	in	exchange for	avoiding	passing	the	choice	of	whether	to	accept	the	bet	to	j. Proof: Assume	0	<	c(P)	<	1	and	let	us	rescale	i's	utility	function	so	that	the	payment	i	receives	by	choosing	to	accept the	bet	in	case	P	is	true	is	1,	and	the	payment	i	receives	by	choosing	to	accept	the	bet	in	case	P	is	false	is	0. 17 Thus,	i's	expected	utility	from	accepting	the	bet	is	c(P).	If	i	chooses	to	reject	the	bet	he	gets	a	payment	of 0<a<c(P).	Thus,	i	prefers	accepting	the	bet	to	rejecting	it. Now	let	Y	=	"j's	degree	of	belief	in	P	is	lower	than	or	equal	to	a".	Since	j	is	rational	and	sympathetic,	in	case	Y is	true	(i.e.	in	case	j's	degree	of	belief	in	P	is	lower	than	or	equal	to	a),	j	will	choose	to	reject	the	bet.	Similarly, in	case	-Y	is	true	(i.e.	in	case	j's	degree	of	belief	in	P	is	higher	than	a),	j	will	choose	to	accept	the	bet. Let	L	be	the	act	of	letting	j	choose	whether	to	accept	the	bet,	and	let	¬L	be	the	act	of	rejecting	the	offer	to let	j	choose	whether	to	accept	the	bet.	We	saw	that	i's	expected	utility	from	¬L	is	just	the	expected	utility	of the	bet,	which	is	c(P).	We	can	now	rewrite	c(P)	using	the	Theorem	of	Total	Probability	applied	to	the	partition {Y,-Y}: 4. EU(¬L)	=	c(P)	=	c(P|-Y)c(-Y)	+	c(P|Y)c(Y) What	is	the	expected	utility	of	L? 5. EU(L)	=	c(P|-Y)c(-Y)	+	ac(Y) In	words:	i's	expected	utility	from	passing	the	choice	on	to	j	equals	the	probability	i	assigns	to	the	possibility that	j	will	accept	the	bet	multiplied	by	the	expected	utility	of	the	bet	from	the	point	of	view	of	i	after	learning that	j	choses	to	accept	the	bet	(i.e.	c(P|-Y))	plus	the	probability	i	assigns	to	the	possibility	of	j	rejecting	the bet	multiplied	by	the	expected	utility	of	rejecting	the	bet	(i.e.	a). i	will	choose	to	pass	the	choice	on	to	j	iff	EU(¬L)	≤	EU(L).	Thus,	it	immediately	follows	from	4	and	5	that	if	c(Y) >	0,	i	chooses	to	pass	the	choice	on	to	j	iff	a	>	c(P|Y). Let	Y*	be	the	set	of	all	propositions	of	the	form	"j's	degree	of	belief	in	P	is	xi"	such	that	xi	≤	a,	to	which	i assigns	a	positive	probability.	In	other	words,	Y	is	the	disjunction	of	all	the	propositions	in	Y*.	We	assume that	Y*	is	countable.	We	suspect	that	a	similar	theorem	to	the	one	we	present	here	can	be	proved	for	the uncountable	case	(this	becomes	clear	by	considering	the	rest	of	the	proof).	However,	our	characterization of	the	LP	view	is	not	well-defined	in	the	uncountable	infinite	case	(in	which	typically	each	proposition	gets	a 0	probability)	and	we	believe	that	the	theoretical	cost	involved	in	the	philosophical	interpretation	of	a characterization	which	is	mathematically	well-defined	also	in	the	uncountable	case	outweighs	the	benefits associated	with	such	a	characterization.	This	is	so	since	a	position	according	to	which	LP	is	true	only	in	the case	in	which	i	assigns	positive	probabilities	to	uncountably	many	hypothesis	regarding	j's	degree	of	belief in	P,	seems	unmotivated.	If	LP	is	true,	it	must	be	true	also	in	the	countable	case	(indeed,	also	for	the	finite 18 case),	it	seems	to	us.	Thus,	proving	the	theorem	for	the	countable	case	is	enough	for	the	philosophical	goal we	have	set	for	ourselves. Now,	since,	by	definition	Y	is	the	disjunction	of	all	the	propositions	in	Y*	(we	assume,	of	course,	that	all	the propositions	in	Y*	are	disjoint,	i.e.	that	j's	degree	of	belief	in	P	is	unique): 6. c P Y = ! $."/"01∗ ! 3 = ! $|." ! ."/"01∗ ! 3 However,	from	LP,	for	each	Xi,	c(P|Xi)	=	wc(P)	+	(1-w)xi.	Thus: 7. c P Y = ! ." 5! 6 '(785)("/"01∗ ! 3 = wc p + (1 − w) ! ." ("/"01∗ ! 3 Let	us	now	define	Z = ! ." ("/"01∗ ! 3 and	we	get: 8. c(P|Y)	=	wc p + (1 − w)Z Notice	that	Z	is	a	weighted	average	of	all	xi	in	Y*	and	thus	is	lower	than	a	(or	equal	to	it	in	the	case	in	which Y*	includes	only	one	proposition:	"j	believes	P	to	degree	a").	Similarly	c(P|Y)	must	be	strictly	lower	than c(P). We	are	interested	in	the	expression	"a	–	c(P|Y)".	We	want	to	show	that	for	some	values	of	a	such	that	c(P) >	a	>	0,	and	c(Y)	>	0,	this	expression	is	positive	and	for	some	values	it	is	negative	independently	of	w.	If	this is	the	case	then,	independently	of	the	weight,	there	are	always	bets	such	that	EU(-L)	>	EU(L)	and	bets	such that	EU(L)	>	EU(-L). a	–	c(P|Y)	<	0 Case	1: if	there	is	an	x*	which	is	the	lowest	value	for	j's	degree	of	belief in	P	to	which	i	assigns	a	positive probability,	set	a=x*	(so	that	c(Y)	>0).	From	the	LP	formula	we	get: 9. c(P|Y)	=wc(P)	+	(1-w)a and	since	a	<	c(P),	it	immediately	follows	that	c(P|Y)	>	a	and	so	a-c(P|Y)	is	negative. 19 Case	2:	If	there	is	no	x*	which	is	the	lowest	value	for	j's	degree	of	belief in	P	to	which	i	assigns	a	positive probability,	then	pick	an	a	such	that	a	<	w?c(P), and	then	(from	equation	8): 10. c(P|Y)	=	wc(P)	+ (1 − w)Z > a and	trivially	ac(P|Y)	<	0	and	c(Y)	>	0	(since	there	is	no	lowest	x*).21 a	–	c(P|Y)	>	0: Let	V	be	the	propositions	"j's	degree	of	belief	in	P	is	lower	than	c(P)"	and	let	V*	be	the	set	of	all	propositions of	the	form	"j's	degree	of	belief	in	P	is	xi"	such	that	xi	<	c(P)	(i.e.	V	is	the	disjunction	of	all	the	propositions	in V*).	Let	us	now	define	Z*	= ! ." ("/"0@∗ ! A .	Notice	that	Z*	is	a	weighted	average	of	all	xi	in	V*	and	thus	is	strictly lower	than	c(P). Now	set: a	=	wc P +(1 − w)Z* With	such	an	a,	it	follows	from	equation	8	that 11. a	–	c(P|Y)	= (1 − w)(Z*	Z) However,	since	a	<	c(P),	(Z*	Z) ≥	0. Case	1:	there	is	a	Xi	in	V*	such	that	xi	>	wc P +(1 − w)Z*.	In	such	a	case	clearly	(Z*	Z)	>	0	and	thus a	–	c(P|Y)	>	0	. Case	2:	there	is	no	such	Xi.	In	such	a	case	there	exists	a	Xi	in	V*	with	the	highest	xi	of	all	the	xis	in	all	the	Xis	in V* (in other	words there exists a hypothesis about j's degree of belief in P to	which i assigns a positive probability	that	assigns	to	j	the	maximal	degree	of	belief	in	P	which	is	strictly	lower	that	c(P)).	Let	us	call	this xi,	x**.	By	the	definition	of	Y,	c(P|Y)	is	equal	for	all	values	of	a	as	long	as	a	>	x**	and	so	it	is	always	possible to	find	a	high-enough	a	such	that	c(P)	>	a	>	c(P|Y).	In	this	case	c(Y)	>	0	is	trivially	true. 21 We	thank	an	anonymous	referee	for	suggesting	this	move. 20 This	concludes	the	proof. References Anders-Levinstein,	Benjamin	(2015),	With	All	Due	Respect:	The	Macro-Epistemology	of	Disagreement, Philosophers'	Imprint,	15	(13),	1-20. Bradley,	R.	(2007),	Reaching	a	Consensus,	Social	Choice	and	Welfare,	29,	609–632. Christensen,	D.	(2007),	Epistemology	of	Disagreement:	The	Good	News,	Philosophical	Review,	116,	187	–	217. Christensen, David (2011) Disagreement, Question-Begging, and Epistemic Self-Criticism, Philosophers' Imprint	11	(6). Cohen,	Stewart	(2013),	A	Defense	of	the	(Almost)	Equal	Weight	View,	In	David	Christensen	&	Jennifer	Lackey (eds.),	The	Epistemology	of	Disagreement. Dietrich, F. and List. C. (2014), Probabilistic Opinion Pooling, in Oxford Handbook of Probability and Philosophy,	Forthcoming. Elga,	A.	(2007),	Reflection	and	Disagreement,	Nous,	XLI(3):478–502. Jehle,	D.,	and	Fitelson,	B.	(2009).	What	is	the	"Equal	Weight	View"? Episteme,	6:3.	280–93. Kelly,	Thomas	(2010).	Peer	disagreement	and	higher	order	evidence.	In	Alvin	I.	Goldman	&	Dennis	Whitcomb (eds.),	Social	Epistemology:	Essential	Readings.	Oxford	University	Press.	pp.	183--217. Keren,	A.	(2007).	Epistemic	Authority,	Testimony	and	the	Transmission	of	Knowledge.	Episteme,	4(3),	368381. Lackey,	Jennifer	&	Christensen,	David	(eds.)	(2013).	The	Epistemology	of	Disagreement:	New	Essays.	Oxford University	Press. Lasonen-Aarino,	M.	(2013),	Disagreement	and	Evidential	Attenuation,	Nous,	47:4,767-94. 21 Lehrer,	K	and	Wagner,	C.	(1981),	Rational	consensus	in	science	and	society,	Dordrecht:	Reidel. Lewis,	D.	(1980):	A	Subjectivist's	Guide	to	Objective	Chance, in	R.	C.	Jeffrey	(ed.),	1980,	Studies in Inductive	Logic	and	Probabilities,	Vol.	II,	Berkeley:	University	of	California	Press,	pp.	263-93. Shogenji, T. (2007), My way or her way: A Conundrum in Bayesian Epistemology of Disagreement. Unpublished	manuscript. Steele,	K.	S.	(2012),	Testimony	as	evidence:	more	problems	for	linear	pooling,	Journal	of	Philosophical	Logic, 41:6,	983-99. Wilson,	A.	(2010),	Disagreement,	equal	weight	and	commutativity,	Philosophical	Studies,	149:3,	321-6. Acknowledgments normative	and	belief	rational	on	workshop	Haifa	the	in	presented	were	paper	this	of	versions	Earlier Sweden	sity,Univer	Stockholm	Philosophy,	of	Department	,Seminar	Higher	Stockholm	),(2017	commitment November	(2015).	We	thank	the	participants	of	these	events	for	useful	discussions.	We	especially	want	to thank	David	Enoch,	Zeev	Goldschmidt,	Noam	Nisan,	Orri	Schneebaum,	and	two	anonymous	referees	for	their very	useful	comments	and	suggestions	as	well	as	an	anonymous	referee	from	another	journal.	Levi	Spectre's research	was	supported	by	the	Israeli	Science	Foundation	(Grant	No.	463/12).